LCD Least Common Denominator
● Free Practice Worksheet

Least Common Denominator Practice Problems

Thirty least common denominator problems split across three difficulty levels, from single-digit denominators to three-fraction and mixed-number challenges. Every answer is fully worked out. Click a problem to reveal the reasoning, not just the final number.

30practice problems
3difficulty levels
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01. BEGINNER Denominators under 10

Beginner LCD Practice

Start here if you are new to finding the least common denominator. Every problem below uses denominators smaller than 10, so listing multiples by hand is quick. Click any problem to reveal the full reasoning behind its answer.

Find the LCD of 1/2 and 1/3.
List the multiples of each denominator: 2 → 2, 4, 6, 8… and 3 → 3, 6, 9, 12… The smallest number that appears in both lists is 6, so the LCD of 1/2 and 1/3 is 6. Rewritten with the common denominator, the fractions become 3/6 and 2/6.
Find the LCD of 1/4 and 1/6.
Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18… The first shared value is 12, so the LCD is 12. As a check, 4 × 3 = 12 and 6 × 2 = 12, confirming 1/4 = 3/12 and 1/6 = 2/12.
Find the LCD of 2/3 and 1/4.
3 and 4 share no factors other than 1, so their LCD is simply their product: 3 × 4 = 12. Listing multiples confirms it: 3, 6, 9, 12 and 4, 8, 12, with 12 being the first common value. 2/3 becomes 8/12 and 1/4 becomes 3/12.
Find the LCD of 1/6 and 1/9.
Multiples of 6: 6, 12, 18, 24… Multiples of 9: 9, 18, 27… The lowest shared multiple is 18, so the LCD is 18. That makes 1/6 = 3/18 and 1/9 = 2/18.
Find the LCD of 3/4 and 2/5.
4 and 5 have no common factors besides 1, so multiply them directly: 4 × 5 = 20. Checking multiples of 4 (4, 8, 12, 16, 20) and 5 (5, 10, 15, 20) confirms 20 is the first match. 3/4 becomes 15/20 and 2/5 becomes 8/20.
Find the LCD of 1/8 and 1/4.
Before listing multiples, check whether one denominator divides the other. That shortcut works here. Since 4 divides evenly into 8 (8 ÷ 4 = 2), the larger denominator is already the LCD. The LCD of 1/8 and 1/4 is 8, and 1/4 simply becomes 2/8.
Find the LCD of 2/3 and 3/5.
3 and 5 share no common factors, so the LCD is their product: 3 × 5 = 15. Multiples of 3 (3, 6, 9, 12, 15) and multiples of 5 (5, 10, 15) meet first at 15. 2/3 becomes 10/15 and 3/5 becomes 9/15.
Find the LCD of 5/6 and 3/4.
Multiples of 6: 6, 12, 18, 24… Multiples of 4: 4, 8, 12, 16, 20, 24… The smallest common value is 12, so the LCD is 12. That gives 5/6 = 10/12 and 3/4 = 9/12.
Find the LCD of 1/2 and 2/7.
2 and 7 have no shared factors, so multiply them: 2 × 7 = 14. Multiples of 2 (2, 4, 6, 8, 10, 12, 14) and 7 (7, 14) both reach 14 first. 1/2 becomes 7/14 and 2/7 becomes 4/14.
Find the LCD of 3/8 and 1/6.
Multiples of 8: 8, 16, 24, 32… Multiples of 6: 6, 12, 18, 24, 30… The first common multiple is 24, so the LCD is 24. That makes 3/8 = 9/24 and 1/6 = 4/24.
02. INTERMEDIATE Denominators 10–30

Intermediate LCD Practice

These ten problems use denominators between 10 and 30, so listing multiples by hand becomes slow. Each worked answer shows the prime-factorization method instead, breaking every denominator down and combining the highest power of each prime.

Find the LCD of 5/12 and 7/18.
Break each denominator into prime factors: 12 = 2² × 3 and 18 = 2 × 3². The LCD needs the highest power of every prime that appears, 2² and 3², so LCD = 4 × 9 = 36. That converts the fractions to 15/36 and 14/36.
Find the LCD of 3/10 and 4/15.
10 = 2 × 5 and 15 = 3 × 5. Taking the highest power of each prime present (2, 3, and 5) gives LCD = 2 × 3 × 5 = 30. So 3/10 becomes 9/30 and 4/15 becomes 8/30.
Find the LCD of 7/20 and 5/24.
20 = 2² × 5 and 24 = 2³ × 3. Using the highest power of each prime, 2³, 3¹, and 5¹, the LCD is 8 × 3 × 5 = 120. That makes 7/20 = 42/120 and 5/24 = 25/120.
Find the LCD of 5/16 and 3/12.
16 = 2⁴ and 12 = 2² × 3. The LCD takes 2⁴ (the higher power of 2) and 3¹, giving 16 × 3 = 48. So 5/16 becomes 15/48 and 3/12 becomes 12/48.
Find the LCD of 9/25 and 4/15.
25 = 5² and 15 = 3 × 5. The LCD needs 5² (the higher power of 5) and 3¹, so LCD = 25 × 3 = 75. That gives 9/25 = 27/75 and 4/15 = 20/75.
Find the LCD of 7/18 and 5/24.
18 = 2 × 3² and 24 = 2³ × 3. Taking the highest powers, 2³ and 3², the LCD is 8 × 9 = 72. So 7/18 becomes 28/72 and 5/24 becomes 15/72.
Find the LCD of 11/30 and 7/20.
30 = 2 × 3 × 5 and 20 = 2² × 5. The LCD needs 2², 3¹, and 5¹, which multiplies out to 4 × 3 × 5 = 60. That converts the fractions to 22/60 and 21/60.
Find the LCD of 5/14 and 3/21.
14 = 2 × 7 and 21 = 3 × 7. Since both share the factor 7, the LCD only needs one copy of it: 2 × 3 × 7 = 42. So 5/14 becomes 15/42 and 3/21 becomes 6/42.
Find the LCD of 4/27 and 5/18.
27 = 3³ and 18 = 2 × 3². The LCD takes the higher power of 3 (3³) along with the 2 from 18, giving 27 × 2 = 54. That makes 4/27 = 8/54 and 5/18 = 15/54.
Find the LCD of 7/22 and 5/11.
22 = 2 × 11, and 11 divides evenly into 22, so the larger denominator is already the LCD: 22. That converts 5/11 into 10/22, while 7/22 stays as it is.
03. ADVANCED 3 fractions & mixed numbers

Advanced LCD Practice

The final set of ten problems steps beyond pairs of fractions: some ask for the LCD of three fractions at once, and others require finding the LCD of the fractional parts of mixed numbers before adding or comparing them.

Find the LCD of 1/2, 1/3, and 1/4.
With three denominators, find the LCM of all of them at once. 2 = 2, 3 = 3, 4 = 2². The LCD needs 2² and 3¹, so LCD = 4 × 3 = 12. The fractions become 6/12, 4/12, and 3/12.
Find the LCD of 2/3, 3/4, and 5/6.
3 = 3, 4 = 2², 6 = 2 × 3. The highest powers present are 2² and 3¹, giving an LCD of 4 × 3 = 12. That converts the set to 8/12, 9/12, and 10/12.
Find the LCD of 1/5, 1/6, and 1/15.
5 = 5, 6 = 2 × 3, 15 = 3 × 5. Combining every prime at its highest power, 2¹, 3¹, and 5¹, gives an LCD of 2 × 3 × 5 = 30. The fractions become 6/30, 5/30, and 2/30.
Add 2 1/4 and 1 1/6 using the LCD.
Only the fractional parts need a common denominator, so find the LCD of 4 and 6. 4 = 2², 6 = 2 × 3, so the LCD is 2² × 3 = 12. That makes 1/4 = 3/12 and 1/6 = 2/12, so 2 1/4 + 1 1/6 = 2 3/12 + 1 2/12 = 3 5/12.
Compare 3 5/8 and 1 3/4 using the LCD.
The denominators are 8 and 4. Since 4 divides evenly into 8, the LCD is simply 8. Converting 3/4 to eighths gives 1 6/8, so the comparison becomes 3 5/8 versus 1 6/8, both now sharing the denominator 8.
Find the LCD of 1/2, 2/9, and 5/12.
2 = 2, 9 = 3², 12 = 2² × 3. Taking the highest power of every prime, 2² and 3², the LCD is 4 × 9 = 36. The fractions become 18/36, 8/36, and 15/36.
Add 4 2/5, 2 3/10, and 1 1/4 using the LCD.
The fractional denominators are 5, 10, and 4. 5 = 5, 10 = 2 × 5, 4 = 2². The LCD needs 2² and 5¹, giving 4 × 5 = 20. That turns the fractions into 8/20, 6/20, and 5/20 before adding the whole numbers.
Find the LCD of 3/7, 2/14, and 5/21.
7 = 7, 14 = 2 × 7, 21 = 3 × 7. Every denominator shares the factor 7, so the LCD only needs one copy of it along with 2 and 3: 2 × 3 × 7 = 42. The fractions become 18/42, 6/42, and 10/42.
Add 5 1/6, 3 2/9, and 2 1/3 using the LCD.
The fractional denominators are 6, 9, and 3. 6 = 2 × 3, 9 = 3², 3 = 3. The LCD needs 2¹ and 3², giving 2 × 9 = 18. That converts the fractions to 3/18, 4/18, and 6/18 before combining the whole numbers.
Find the LCD of 3/16, 5/24, and 7/36.
16 = 2⁴, 24 = 2³ × 3, 36 = 2² × 3². Taking the highest power of each prime, 2⁴ and 3², the LCD is 16 × 9 = 144. The fractions become 27/144, 30/144, and 28/144.
04. TIPS

5 Tips for Solving LCD Problems Faster

These five habits are what separate a slow multiple-by-multiple search from an answer in seconds. Work them into your practice routine above and speed follows naturally.

  1. Check if one denominator divides the other first. Before listing a single multiple, divide the larger denominator by the smaller one. If it comes out even, the larger denominator is already the LCD, and no further work is needed. This shortcut solves a surprising number of problems in seconds, as with 1/4 and 1/8 (LCD = 8) or 1/3 and 2/9 (LCD = 9).
  2. Use prime factorization for large denominators. Once denominators climb past 12 or so, listing multiples by hand gets slow and error-prone. Break each denominator into its prime factors instead, then build the LCD from the highest power of every prime that appears across all of them. It scales cleanly to any number of fractions.
  3. The LCD is never smaller than the largest denominator. Use this as a built-in sanity check. If a calculated answer comes out smaller than the biggest denominator in the problem, a mistake was made somewhere. The LCD must always be at least as large as the largest denominator you started with.
  4. Practice times tables for faster multiple listing. Fluency with times tables through 12 turns multiple-listing from a slow, step-by-step process into instant recall. The faster you can generate 6, 12, 18, 24, 30… in your head, the faster every LCD problem with small-to-medium denominators becomes.
  5. Use the GCF formula: LCD = (a × b) ÷ GCF(a, b). For two denominators, find their greatest common factor first, then apply LCD = (a × b) ÷ GCF(a, b). For 8 and 12, the GCF is 4, so the LCD is (8 × 12) ÷ 4 = 24, matching the answer you would get from listing multiples, but in one calculation.
05. FAQ

LCD Practice: Frequently Asked Questions

What grade level is LCD taught?
In most U.S. curricula, the least common denominator is introduced in 4th grade alongside equivalent fractions, then used heavily in 5th grade for adding and subtracting fractions with unlike denominators. It resurfaces in middle-school pre-algebra and again in algebra courses whenever rational expressions need a common denominator.
How do I get faster at finding the LCD?
Speed comes from pattern recognition, not memorization. Learn times tables through 12, always check whether one denominator divides the other before doing any extra work, and switch to prime factorization once a denominator is too large to list multiples of quickly. Working through a mix of beginner, intermediate, and advanced problems builds that recognition fastest.
What is the LCD of 3/8 and 5/12?
Break both denominators into primes: 8 = 2³ and 12 = 2² × 3. The LCD needs the highest power of every prime that appears, 2³ and 3¹, which multiplies out to 24. So 3/8 becomes 9/24 and 5/12 becomes 10/24.
Can the LCD equal one of the denominators?
Yes. Whenever one denominator divides evenly into the other, the larger of the two is automatically the LCD and no extra multiplication is needed. That is the case with 1/4 and 1/8, where the LCD is 8, or with 1/3 and 2/9, where the LCD is 9.
How many practice problems should I do to get good at finding the LCD?
Most students reach comfortable fluency after 30 to 50 problems spread across a few difficulty levels, which is why this page includes 10 beginner, 10 intermediate, and 10 advanced problems. Revisiting missed problems a day or two later cements the skill far better than repeating the same set immediately.