LCM for 3, 4 and 10

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 4 and 10?

Answer

LCM of 3, 4 and 10 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 3 = 20, 60 ÷ 4 = 15, 60 ÷ 10 = 6 — and 20, 15 and 6 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 20 and of y/4 by 15 and of z/10 by 6.

3 — prime

4 = 22

10 = 2 × 5

Prime3410Highest power
2—22222
33——3
5——55

— = 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 = 60

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LCM Table

1st2nd3rdLCM
13412
23412
33412
34412
34560
34612
34784
34824
34936
341060
3411132
341212
3413156
341484
341560
341648
3417204
341836
3419228
342060
342184
3422132
3423276
342424
3425300
3426156
3427108
342884
3429348
343060

FAQ

What's the Least Common Multiple (LCM) of 3, 4 and 10?

LCM of 3, 4 and 10 is 60

How to find the LCM of 3, 4 and 10 by prime factorization?

Take every prime that appears in 3, 4 and 10 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 3, 4 and 10 two numbers at a time?

Yes. The LCM of 3 and 4 is 12, and the LCM of 12 and 10 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 3, 4 and 10?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 3, 60 ÷ 4 and 60 ÷ 10 all come out whole. Any other common multiple of 3, 4 and 10 is a multiple of 60.

See Also