LCM for 18, 24 and 60

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What's the Least Common Multiple (LCM) of 18, 24 and 60?

Answer

LCM of 18, 24 and 60 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by all three: 360 ÷ 18 = 20, 360 ÷ 24 = 15, 360 ÷ 60 = 6 — and 20, 15 and 6 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/18 by 20 and of y/24 by 15 and of z/60 by 6.

18 = 2 × 32

24 = 23 × 3

60 = 22 × 3 × 5

Prime182460Highest power
22232223
3323332
5——55

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

LCM = 23 × 32 × 5 = 360

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LCM Table

1st2nd3rdLCM
182445360
1824461,656
1824473,384
182448144
1824493,528
1824501,800
1824511,224
182452936
1824533,816
182454216
1824553,960
182456504
1824571,368
1824582,088
1824594,248
182460360
1824614,392
1824622,232
182463504
182464576
1824654,680
182466792
1824674,824
1824681,224
1824691,656
1824702,520
1824715,112
18247272
1824735,256
1824742,664

FAQ

What's the Least Common Multiple (LCM) of 18, 24 and 60?

LCM of 18, 24 and 60 is 360

How to find the LCM of 18, 24 and 60 by prime factorization?

Take every prime that appears in 18, 24 and 60 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 18, 24 and 60 two numbers at a time?

Yes. The LCM of 18 and 24 is 72, and the LCM of 72 and 60 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 18, 24 and 60?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 18, 360 ÷ 24 and 360 ÷ 60 all come out whole. Any other common multiple of 18, 24 and 60 is a multiple of 360.

See Also