LCM for 12, 28 and 36

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What's the Least Common Multiple (LCM) of 12, 28 and 36?

Answer

LCM of 12, 28 and 36 is
252

First common multiples: 252, 504, 756, …

252 is divisible by all three: 252 ÷ 12 = 21, 252 ÷ 28 = 9, 252 ÷ 36 = 7 — and 21, 9 and 7 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/12 by 21 and of y/28 by 9 and of z/36 by 7.

12 = 22 × 3

28 = 22 × 7

36 = 22 × 32

Prime122836Highest power
222222222
33—3232
7—7—7

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

LCM = 22 × 32 × 7 = 252

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LCM Table

1st2nd3rdLCM
12212884
122228924
1223281,932
122428168
1225282,100
1226281,092
122728756
12282884
1228292,436
122830420
1228312,604
122832672
122833924
1228341,428
122835420
122836252
1228373,108
1228381,596
1228391,092
122840840
1228413,444
12284284
1228433,612
122844924
1228451,260
1228461,932
1228473,948
122848336
122849588
1228502,100

FAQ

What's the Least Common Multiple (LCM) of 12, 28 and 36?

LCM of 12, 28 and 36 is 252

How to find the LCM of 12, 28 and 36 by prime factorization?

Take every prime that appears in 12, 28 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

Can you get the LCM of 12, 28 and 36 two numbers at a time?

Yes. The LCM of 12 and 28 is 84, and the LCM of 84 and 36 is 252 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 252 divisible by 12, 28 and 36?

Yes, and by definition it is the smallest positive integer that is: 252 ÷ 12, 252 ÷ 28 and 252 ÷ 36 all come out whole. Any other common multiple of 12, 28 and 36 is a multiple of 252.

See Also