LCM for 24, 28 and 42

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What's the Least Common Multiple (LCM) of 24, 28 and 42?

Answer

LCM of 24, 28 and 42 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 24 = 7, 168 ÷ 28 = 6, 168 ÷ 42 = 4 — and 7, 6 and 4 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/24 by 7 and of y/28 by 6 and of z/42 by 4.

24 = 23 × 3

28 = 22 × 7

42 = 2 × 3 × 7

Prime242842Highest power
22322223
33—33
7—777

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

LCM = 23 × 3 × 7 = 168

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LCM Table

1st2nd3rdLCM
2427281,512
242828168
2428294,872
242830840
2428315,208
242832672
2428331,848
2428342,856
242835840
242836504
2428376,216
2428383,192
2428392,184
242840840
2428416,888
242842168
2428437,224
2428441,848
2428452,520
2428463,864
2428477,896
242848336
2428491,176
2428504,200
2428512,856
2428522,184
2428538,904
2428541,512
2428559,240
242856168

FAQ

What's the Least Common Multiple (LCM) of 24, 28 and 42?

LCM of 24, 28 and 42 is 168

How to find the LCM of 24, 28 and 42 by prime factorization?

Take every prime that appears in 24, 28 and 42 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 24, 28 and 42 two numbers at a time?

Yes. The LCM of 24 and 28 is 168, and the LCM of 168 and 42 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 24, 28 and 42?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 24, 168 ÷ 28 and 168 ÷ 42 all come out whole. Any other common multiple of 24, 28 and 42 is a multiple of 168.

See Also