LCM of 14 and 21
The least common multiple of 14 and 21 is 42 — the smallest positive number into which both 14 and 21 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 42.
14 and 21 share the factor 7, so their first meeting point comes earlier than the raw product: the LCM is (14 × 21) ÷ 7 = 294 ÷ 7 = 42. Both numbers divide it exactly — 14 fits 3 times and 21 fits 2 times — and the pairing identity LCM × GCF = a × b holds again: 42 × 7 = 294. After 42, the lines re-synchronize for good, so the common multiples continue 84, 126, 168, and onward.
| # | Common multiple |
|---|---|
| 1 | 42 |
| 2 | 84 |
| 3 | 126 |
| 4 | 168 |
| 5 | 210 |
| 6 | 252 |
| 7 | 294 |
| 8 | 336 |
| 9 | 378 |
| 10 | 420 |
| 11 | 462 |
| 12 | 504 |
Frequently asked questions
What is the LCM of 14 and 21?
The least common multiple of 14 and 21 is 42. The multiples of 14 begin 14, 28, 42, 56, … and the multiples of 21 begin 21, 42, 63, …, and 42 is the first value both lists share. Formula check: (14 × 21) ÷ GCF(14, 21) = 294 ÷ 7 = 42.
How do you find the LCM of 14 and 21?
Compare prime factorizations: 14 = 2 × 7 and 21 = 3 × 7. Carry every prime at its highest power into the answer: 2 × 3 × 7 = 42. The shortcut through the GCF lands on the same value: (14 × 21) ÷ 7 = 42.
What is the GCF of 14 and 21?
7. The largest number dividing both. The identity GCF × LCM = 14 × 21 checks it against this page: 7 × 42 = 294. The same GCF reduces fractions built on 14 and 21, while 42 is the common denominator that needs no reducing.
What are the common multiples of 14 and 21?
Exactly the multiples of the LCM: 42, 84, 126, 168, 210, 252, and onward without end. The table above lists the first twelve; every later one is another 42 steps out. These are the numbers into which both 14 and 21 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.