LCM for 24, 36 and 48

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What's the Least Common Multiple (LCM) of 24, 36 and 48?

Answer

LCM of 24, 36 and 48 is
144

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 24 = 6, 144 ÷ 36 = 4, 144 ÷ 48 = 3 — and 6, 4 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/24 by 6 and of y/36 by 4 and of z/48 by 3.

24 = 23 × 3

36 = 22 × 32

48 = 24 × 3

Prime243648Highest power
223222424
3332332

LCM = 24 × 32 = 144

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LCM Table

1st2nd3rdLCM
243336792
2434361,224
2435362,520
24363672
2436372,664
2436381,368
243639936
243640360
2436412,952
243642504
2436433,096
243644792
243645360
2436461,656
2436473,384
243648144
2436493,528
2436501,800
2436511,224
243652936
2436533,816
243654216
2436553,960
243656504
2436571,368
2436582,088
2436594,248
243660360
2436614,392
2436622,232

FAQ

What's the Least Common Multiple (LCM) of 24, 36 and 48?

LCM of 24, 36 and 48 is 144

How to find the LCM of 24, 36 and 48 by prime factorization?

Take every prime that appears in 24, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 24, 36 and 48 two numbers at a time?

Yes. The LCM of 24 and 36 is 72, and the LCM of 72 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 24, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 24, 144 ÷ 36 and 144 ÷ 48 all come out whole. Any other common multiple of 24, 36 and 48 is a multiple of 144.

See Also