LCM for 4, 8 and 12

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What's the Least Common Multiple (LCM) of 4, 8 and 12?

Answer

LCM of 4, 8 and 12 is
24

First common multiples: 24, 48, 72, …

24 is divisible by all three: 24 ÷ 4 = 6, 24 ÷ 8 = 3, 24 ÷ 12 = 2 — and 6, 3 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/4 by 6 and of y/8 by 3 and of z/12 by 2.

4 = 22

8 = 23

12 = 22 × 3

Prime4812Highest power
222232223
3——33

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

LCM = 23 × 3 = 24

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LCM Table

1st2nd3rdLCM
1488
2488
34824
4488
45840
46824
47856
4888
48972
481040
481188
481224
4813104
481456
4815120
481616
4817136
481872
4819152
482040
4821168
482288
4823184
482424
4825200
4826104
4827216
482856
4829232
4830120

FAQ

What's the Least Common Multiple (LCM) of 4, 8 and 12?

LCM of 4, 8 and 12 is 24

How to find the LCM of 4, 8 and 12 by prime factorization?

Take every prime that appears in 4, 8 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 = 24.

Can you get the LCM of 4, 8 and 12 two numbers at a time?

Yes. The LCM of 4 and 8 is 8, and the LCM of 8 and 12 is 24 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 24 divisible by 4, 8 and 12?

Yes, and by definition it is the smallest positive integer that is: 24 ÷ 4, 24 ÷ 8 and 24 ÷ 12 all come out whole. Any other common multiple of 4, 8 and 12 is a multiple of 24.

See Also