Skip the scratch paper. This page collects every LCD lookup a student, parent, or teacher is likely to need in one place: a full pairwise grid for denominators 2 through 10, a quick-reference table of commonly searched LCM pairs up to 20, a complete prime factorization chart from 2 to 30, and a printable four-step anchor chart for solving LCD problems by hand. Every value below is calculated programmatically rather than typed by hand, so the numbers are guaranteed to be correct.
The grid below covers every combination of denominators from 2 through 10: 9 rows by 9 columns, 81 pairings in total. These small denominators are exactly the ones that show up over and over in real fraction problems, from recipe conversions to algebra homework, so a single dense chart is far more useful than a long list of isolated examples. To read it, find your first denominator down the left side and your second denominator across the top, then look at the cell where the row and column meet. That bolded number is the least common denominator for that pair. On a phone or narrow window the table scrolls horizontally, so nothing gets cut off or squeezed.
| A \ B | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| 2 | 2 | 6 | 4 | 10 | 6 | 14 | 8 | 18 | 10 |
| 3 | 6 | 3 | 12 | 15 | 6 | 21 | 24 | 9 | 30 |
| 4 | 4 | 12 | 4 | 20 | 12 | 28 | 8 | 36 | 20 |
| 5 | 10 | 15 | 20 | 5 | 30 | 35 | 40 | 45 | 10 |
| 6 | 6 | 6 | 12 | 30 | 6 | 42 | 24 | 18 | 30 |
| 7 | 14 | 21 | 28 | 35 | 42 | 7 | 56 | 63 | 70 |
| 8 | 8 | 24 | 8 | 40 | 24 | 56 | 8 | 72 | 40 |
| 9 | 18 | 9 | 36 | 45 | 18 | 63 | 72 | 9 | 90 |
| 10 | 10 | 30 | 20 | 10 | 30 | 70 | 40 | 90 | 10 |
The least common multiple and the least common denominator are the same calculation applied to two different situations. LCM works on whole numbers, while LCD applies that identical result to the denominators of a fraction problem. The pairs below extend past the 2–10 grid above into the 10–20 range, covering the number combinations that come up most often once students start working with tenths, twelfths, fifteenths, and twentieths, think measurement conversions, class scheduling problems, or splitting a group into uneven teams. Use this table exactly like the one above: match your two numbers, then read off the LCM in the third column.
| Number A | Number B | LCM |
|---|---|---|
| 10 | 12 | 60 |
| 10 | 15 | 30 |
| 12 | 15 | 60 |
| 12 | 16 | 48 |
| 12 | 18 | 36 |
| 12 | 20 | 60 |
| 14 | 20 | 140 |
| 15 | 18 | 90 |
| 15 | 20 | 60 |
| 16 | 20 | 80 |
| 9 | 15 | 45 |
| 8 | 12 | 24 |
| 6 | 16 | 48 |
| 10 | 20 | 20 |
| 18 | 20 | 180 |
Notice how much the answer depends on shared factors: 15 and 20 both split evenly by 5, so their LCM (60) is much smaller than their product (300), while a pair like 9 and 15 shares only the factor 3 and lands on an LCM of 45. Spotting the shared factor before you multiply is the fastest way to simplify LCD work by hand.
Every LCD and LCM calculation is really just prime factorization in disguise. Once you know which primes build each number, finding a common denominator is a matter of combining the highest power of every prime that appears. The chart below lists the complete prime factorization, in exponent form, for every whole number from 2 through 30. A number written as 12 → 2² × 3 means 12 breaks down into two factors of 2 and one factor of 3; prime numbers themselves, like 7, 11, or 29, have no smaller factors at all, so they're flagged as prime rather than split further.
| Number | Prime Factorization |
|---|---|
| 2 | 2 (prime) |
| 3 | 3 (prime) |
| 4 | 22 |
| 5 | 5 (prime) |
| 6 | 2 × 3 |
| 7 | 7 (prime) |
| 8 | 23 |
| 9 | 32 |
| 10 | 2 × 5 |
| 11 | 11 (prime) |
| 12 | 22 × 3 |
| 13 | 13 (prime) |
| 14 | 2 × 7 |
| 15 | 3 × 5 |
| 16 | 24 |
| 17 | 17 (prime) |
| 18 | 2 × 32 |
| 19 | 19 (prime) |
| 20 | 22 × 5 |
| 21 | 3 × 7 |
| 22 | 2 × 11 |
| 23 | 23 (prime) |
| 24 | 23 × 3 |
| 25 | 52 |
| 26 | 2 × 13 |
| 27 | 33 |
| 28 | 22 × 7 |
| 29 | 29 (prime) |
| 30 | 2 × 3 × 5 |
When a lookup table doesn't cover your exact pair, or when a teacher wants students to show their work, this is the classroom method worth printing and pinning to the wall. It breaks the least common denominator process into four repeatable steps that work for any pair of denominators, no matter how large.
Start by writing the denominator of every fraction in the problem on its own line. This keeps you from losing track of which number belongs to which fraction once the multiples start piling up.
Under each denominator, list its multiples in order: the denominator itself, then double it, triple it, and so on. Keep going until the lists have at least a few numbers in common, or until one list clearly contains a multiple that appears in every other list.
Scan across the lists for the smallest number that shows up in all of them. That value is the least common denominator. It's called "least" because it's the smallest shared multiple, not just any shared multiple.
Divide the LCD by each original denominator to get a multiplier, then multiply both the numerator and denominator of that fraction by it. Once every fraction shares the same bottom number, you can add, subtract, or compare them directly.