LCM of 21 and 28
The least common multiple of 21 and 28 is 84 — the smallest positive number into which both 21 and 28 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 84.
21 and 28 share the factor 7, so their first meeting point comes earlier than the raw product: the LCM is (21 × 28) ÷ 7 = 588 ÷ 7 = 84. Both numbers divide it exactly — 21 fits 4 times and 28 fits 3 times — and the pairing identity LCM × GCF = a × b holds again: 84 × 7 = 588. After 84, the lines re-synchronize for good, so the common multiples continue 168, 252, 336, and onward.
| # | Common multiple |
|---|---|
| 1 | 84 |
| 2 | 168 |
| 3 | 252 |
| 4 | 336 |
| 5 | 420 |
| 6 | 504 |
| 7 | 588 |
| 8 | 672 |
| 9 | 756 |
| 10 | 840 |
| 11 | 924 |
| 12 | 1008 |
Frequently asked questions
What is the LCM of 21 and 28?
The least common multiple of 21 and 28 is 84. The multiples of 21 begin 21, 42, 63, 84, … and the multiples of 28 begin 28, 56, 84, …, and 84 is the first value both lists share. Formula check: (21 × 28) ÷ GCF(21, 28) = 588 ÷ 7 = 84.
How do you find the LCM of 21 and 28?
Compare prime factorizations: 21 = 3 × 7 and 28 = 2² × 7. Carry every prime at its highest power into the answer: 2² × 3 × 7 = 84. The shortcut through the GCF lands on the same value: (21 × 28) ÷ 7 = 84.
What is the GCF of 21 and 28?
7. The largest number dividing both. The identity GCF × LCM = 21 × 28 checks it against this page: 7 × 84 = 588. The same GCF reduces fractions built on 21 and 28, while 84 is the common denominator that needs no reducing.
What are the common multiples of 21 and 28?
Exactly the multiples of the LCM: 84, 168, 252, 336, 420, 504, and onward without end. The table above lists the first twelve; every later one is another 84 steps out. These are the numbers into which both 21 and 28 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.