LCM for 12, 18 and 48

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What's the Least Common Multiple (LCM) of 12, 18 and 48?

Answer

LCM of 12, 18 and 48 is
144

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 12 = 12, 144 ÷ 18 = 8, 144 ÷ 48 = 3 — and 12, 8 and 3 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/12 by 12 and of y/18 by 8 and of z/48 by 3.

12 = 22 × 3

18 = 2 × 32

48 = 24 × 3

Prime121848Highest power
22222424
3332332

LCM = 24 × 32 = 144

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LCM Table

1st2nd3rdLCM
121833396
121834612
1218351,260
12183636
1218371,332
121838684
121839468
121840360
1218411,476
121842252
1218431,548
121844396
121845180
121846828
1218471,692
121848144
1218491,764
121850900
121851612
121852468
1218531,908
121854108
1218551,980
121856504
121857684
1218581,044
1218592,124
121860180
1218612,196
1218621,116

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 48?

LCM of 12, 18 and 48 is 144

How to find the LCM of 12, 18 and 48 by prime factorization?

Take every prime that appears in 12, 18 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 12, 18 and 48 two numbers at a time?

Yes. The LCM of 12 and 18 is 36, and the LCM of 36 and 48 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 12, 18 and 48?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 12, 144 ÷ 18 and 144 ÷ 48 all come out whole. Any other common multiple of 12, 18 and 48 is a multiple of 144.

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