LCM for 18, 24 and 42

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What's the Least Common Multiple (LCM) of 18, 24 and 42?

Answer

LCM of 18, 24 and 42 is
504

First common multiples: 504; 1,008; 1,512; …

504 is divisible by all three: 504 ÷ 18 = 28, 504 ÷ 24 = 21, 504 ÷ 42 = 12 — and 28, 21 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 28 and of y/24 by 21 and of z/42 by 12.

18 = 2 × 32

24 = 23 × 3

42 = 2 × 3 × 7

Prime182442Highest power
2223223
3323332
7——77

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

LCM = 23 × 32 × 7 = 504

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LCM Table

1st2nd3rdLCM
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
182445360
1824461,656
1824473,384
182448144
1824493,528
1824501,800
1824511,224
182452936
1824533,816
182454216
1824553,960
182456504

FAQ

What's the Least Common Multiple (LCM) of 18, 24 and 42?

LCM of 18, 24 and 42 is 504

How to find the LCM of 18, 24 and 42 by prime factorization?

Take every prime that appears in 18, 24 and 42 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 7 = 504.

Can you get the LCM of 18, 24 and 42 two numbers at a time?

Yes. The LCM of 18 and 24 is 72, and the LCM of 72 and 42 is 504 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 504 divisible by 18, 24 and 42?

Yes, and by definition it is the smallest positive integer that is: 504 ÷ 18, 504 ÷ 24 and 504 ÷ 42 all come out whole. Any other common multiple of 18, 24 and 42 is a multiple of 504.

See Also