LCM for 3, 7 and 20

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 7 and 20?

Answer

LCM of 3, 7 and 20 is
420

First common multiples: 420; 840; 1,260; …

420 is divisible by all three: 420 ÷ 3 = 140, 420 ÷ 7 = 60, 420 ÷ 20 = 21 — and 140, 60 and 21 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/3 by 140 and of y/7 by 60 and of z/20 by 21.

3 — prime

7 — prime

20 = 22 × 5

Prime3720Highest power
2——2222
33——3
5——55
7—7—7

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 22 × 3 × 5 × 7 = 420

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LCM Table

1st2nd3rdLCM
357105
36742
37721
378168
37963
3710210
3711231
371284
3713273
371442
3715105
3716336
3717357
3718126
3719399
3720420
372121
3722462
3723483
3724168
3725525
3726546
3727189
372884
3729609
3730210
3731651
3732672
3733231
3734714

FAQ

What's the Least Common Multiple (LCM) of 3, 7 and 20?

LCM of 3, 7 and 20 is 420

How to find the LCM of 3, 7 and 20 by prime factorization?

Take every prime that appears in 3, 7 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 3, 7 and 20 two numbers at a time?

Yes. The LCM of 3 and 7 is 21, and the LCM of 21 and 20 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 3, 7 and 20?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 3, 420 ÷ 7 and 420 ÷ 20 all come out whole. Any other common multiple of 3, 7 and 20 is a multiple of 420.

See Also