LCM for 10, 12 and 24

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What's the Least Common Multiple (LCM) of 10, 12 and 24?

Answer

LCM of 10, 12 and 24 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 10 = 12, 120 ÷ 12 = 10, 120 ÷ 24 = 5 — and 12, 10 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/10 by 12 and of y/12 by 10 and of z/24 by 5.

10 = 2 × 5

12 = 22 × 3

24 = 23 × 3

Prime101224Highest power
22222323
3—333
55——5

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

LCM = 23 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
91012180
10101260
101112660
10121260
101213780
101214420
10121560
101216240
1012171,020
101218180
1012191,140
10122060
101221420
101222660
1012231,380
101224120
101225300
101226780
101227540
101228420
1012291,740
10123060
1012311,860
101232480
101233660
1012341,020
101235420
101236180
1012372,220
1012381,140

FAQ

What's the Least Common Multiple (LCM) of 10, 12 and 24?

LCM of 10, 12 and 24 is 120

How to find the LCM of 10, 12 and 24 by prime factorization?

Take every prime that appears in 10, 12 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 10, 12 and 24 two numbers at a time?

Yes. The LCM of 10 and 12 is 60, and the LCM of 60 and 24 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 10, 12 and 24?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 10, 120 ÷ 12 and 120 ÷ 24 all come out whole. Any other common multiple of 10, 12 and 24 is a multiple of 120.

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