LCM for 16, 18 and 24

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 16, 18 and 24?

Answer

LCM of 16, 18 and 24 is
144

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 16 = 9, 144 ÷ 18 = 8, 144 ÷ 24 = 6 — and 9, 8 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/16 by 9 and of y/18 by 8 and of z/24 by 6.

16 = 24

18 = 2 × 32

24 = 23 × 3

Prime161824Highest power
22422324
3—32332

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

LCM = 24 × 32 = 144

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LCM Table

1st2nd3rdLCM
91618144
101618720
1116181,584
121618144
1316181,872
1416181,008
151618720
161618144
1617182,448
161818144
1618192,736
161820720
1618211,008
1618221,584
1618233,312
161824144
1618253,600
1618261,872
161827432
1618281,008
1618294,176
161830720
1618314,464
161832288
1618331,584
1618342,448
1618355,040
161836144
1618375,328
1618382,736

FAQ

What's the Least Common Multiple (LCM) of 16, 18 and 24?

LCM of 16, 18 and 24 is 144

How to find the LCM of 16, 18 and 24 by prime factorization?

Take every prime that appears in 16, 18 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 16, 18 and 24 two numbers at a time?

Yes. The LCM of 16 and 18 is 144, and the LCM of 144 and 24 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 16, 18 and 24?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 16, 144 ÷ 18 and 144 ÷ 24 all come out whole. Any other common multiple of 16, 18 and 24 is a multiple of 144.

See Also