LCM for 3, 4 and 11

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What's the Least Common Multiple (LCM) of 3, 4 and 11?

Answer

LCM of 3, 4 and 11 is
132

First common multiples: 132, 264, 396, …

132 is divisible by all three: 132 ÷ 3 = 44, 132 ÷ 4 = 33, 132 ÷ 11 = 12 — and 44, 33 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/3 by 44 and of y/4 by 33 and of z/11 by 12.

3 — prime

4 = 22

11 — prime

Prime3411Highest power
2—22—22
33——3
11——1111

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

LCM = 22 × 3 × 11 = 132

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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 11?

LCM of 3, 4 and 11 is 132

How to find the LCM of 3, 4 and 11 by prime factorization?

Take every prime that appears in 3, 4 and 11 to the highest power it reaches in any one of them and multiply: 2² × 3 × 11 = 132.

Can you get the LCM of 3, 4 and 11 two numbers at a time?

Yes. The LCM of 3 and 4 is 12, and the LCM of 12 and 11 is 132 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 132 divisible by 3, 4 and 11?

Yes, and by definition it is the smallest positive integer that is: 132 ÷ 3, 132 ÷ 4 and 132 ÷ 11 all come out whole. Any other common multiple of 3, 4 and 11 is a multiple of 132.

See Also