LCM for 3, 12 and 30

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What's the Least Common Multiple (LCM) of 3, 12 and 30?

Answer

LCM of 3, 12 and 30 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 3 = 20, 60 ÷ 12 = 5, 60 ÷ 30 = 2 — and 20, 5 and 2 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/12 by 5 and of z/30 by 2.

3 — prime

12 = 22 × 3

30 = 2 × 3 × 5

Prime31230Highest power
2—22222
33333
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
3121560
3121648
31217204
3121836
31219228
3122060
3122184
31222132
31223276
3122424
31225300
31226156
31227108
3122884
31229348
3123060
31231372
3123296
31233132
31234204
31235420
3123636
31237444
31238228
31239156
31240120
31241492
3124284
31243516
31244132

FAQ

What's the Least Common Multiple (LCM) of 3, 12 and 30?

LCM of 3, 12 and 30 is 60

How to find the LCM of 3, 12 and 30 by prime factorization?

Take every prime that appears in 3, 12 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 3, 12 and 30 two numbers at a time?

Yes. The LCM of 3 and 12 is 12, and the LCM of 12 and 30 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, 12 and 30?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 3, 60 ÷ 12 and 60 ÷ 30 all come out whole. Any other common multiple of 3, 12 and 30 is a multiple of 60.

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