LCM for 4, 6 and 7

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What's the Least Common Multiple (LCM) of 4, 6 and 7?

Answer

LCM of 4, 6 and 7 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 4 = 21, 84 ÷ 6 = 14, 84 ÷ 7 = 12 — and 21, 14 and 12 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/4 by 21 and of y/6 by 14 and of z/7 by 12.

4 = 22

6 = 2 × 3

7 — prime

Prime467Highest power
2222—22
3—3—3
7——77

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

LCM = 22 × 3 × 7 = 84

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LCM Table

1st2nd3rdLCM
14612
24612
34612
44612
45660
46612
46784
46824
46936
461060
4611132
461212
4613156
461484
461560
461648
4617204
461836
4619228
462060
462184
4622132
4623276
462424
4625300
4626156
4627108
462884
4629348
463060

FAQ

What's the Least Common Multiple (LCM) of 4, 6 and 7?

LCM of 4, 6 and 7 is 84

How to find the LCM of 4, 6 and 7 by prime factorization?

Take every prime that appears in 4, 6 and 7 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 4, 6 and 7 two numbers at a time?

Yes. The LCM of 4 and 6 is 12, and the LCM of 12 and 7 is 84 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 84 divisible by 4, 6 and 7?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 4, 84 ÷ 6 and 84 ÷ 7 all come out whole. Any other common multiple of 4, 6 and 7 is a multiple of 84.

See Also