LCM for 18, 24 and 30

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What's the Least Common Multiple (LCM) of 18, 24 and 30?

Answer

LCM of 18, 24 and 30 is
360

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

360 is divisible by all three: 360 ÷ 18 = 20, 360 ÷ 24 = 15, 360 ÷ 30 = 12 — and 20, 15 and 12 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/30 by 12.

18 = 2 × 32

24 = 23 × 3

30 = 2 × 3 × 5

Prime182430Highest power
2223223
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
151824360
161824144
1718241,224
18182472
1819241,368
182024360
182124504
182224792
1823241,656
18242472
1824251,800
182426936
182427216
182428504
1824292,088
182430360
1824312,232
182432288
182433792
1824341,224
1824352,520
18243672
1824372,664
1824381,368
182439936
182440360
1824412,952
182442504
1824433,096
182444792

FAQ

What's the Least Common Multiple (LCM) of 18, 24 and 30?

LCM of 18, 24 and 30 is 360

How to find the LCM of 18, 24 and 30 by prime factorization?

Take every prime that appears in 18, 24 and 30 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 30 two numbers at a time?

Yes. The LCM of 18 and 24 is 72, and the LCM of 72 and 30 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 30?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 18, 360 ÷ 24 and 360 ÷ 30 all come out whole. Any other common multiple of 18, 24 and 30 is a multiple of 360.

See Also