LCM for 3, 7 and 10

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 7 and 10?

Answer

LCM of 3, 7 and 10 is
210

First common multiples: 210, 420, 630, …

210 is divisible by all three: 210 ÷ 3 = 70, 210 ÷ 7 = 30, 210 ÷ 10 = 21 — and 70, 30 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 70 and of y/7 by 30 and of z/10 by 21.

3 — prime

7 — prime

10 = 2 × 5

Prime3710Highest power
2——22
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 = 2 × 3 × 5 × 7 = 210

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LCM Table

1st2nd3rdLCM
13721
23742
33721
34784
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

FAQ

What's the Least Common Multiple (LCM) of 3, 7 and 10?

LCM of 3, 7 and 10 is 210

How to find the LCM of 3, 7 and 10 by prime factorization?

Take every prime that appears in 3, 7 and 10 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 × 7 = 210.

Can you get the LCM of 3, 7 and 10 two numbers at a time?

Yes. The LCM of 3 and 7 is 21, and the LCM of 21 and 10 is 210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 210 divisible by 3, 7 and 10?

Yes, and by definition it is the smallest positive integer that is: 210 ÷ 3, 210 ÷ 7 and 210 ÷ 10 all come out whole. Any other common multiple of 3, 7 and 10 is a multiple of 210.

See Also