LCM for 4, 10 and 12

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What's the Least Common Multiple (LCM) of 4, 10 and 12?

Answer

LCM of 4, 10 and 12 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 4 = 15, 60 ÷ 10 = 6, 60 ÷ 12 = 5 — and 15, 6 and 5 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 15 and of y/10 by 6 and of z/12 by 5.

4 = 22

10 = 2 × 5

12 = 22 × 3

Prime41012Highest power
22222222
3——33
5—5—5

— = 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
141020
241020
341060
441020
451020
461060
4710140
481040
4910180
4101020
41011220
4101260
41013260
41014140
4101560
4101680
41017340
41018180
41019380
4102020
41021420
41022220
41023460
41024120
41025100
41026260
41027540
41028140
41029580
4103060

FAQ

What's the Least Common Multiple (LCM) of 4, 10 and 12?

LCM of 4, 10 and 12 is 60

How to find the LCM of 4, 10 and 12 by prime factorization?

Take every prime that appears in 4, 10 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 4, 10 and 12 two numbers at a time?

Yes. The LCM of 4 and 10 is 20, and the LCM of 20 and 12 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 4, 10 and 12?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 4, 60 ÷ 10 and 60 ÷ 12 all come out whole. Any other common multiple of 4, 10 and 12 is a multiple of 60.

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