LCM for 16, 36 and 48

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What's the Least Common Multiple (LCM) of 16, 36 and 48?

Answer

LCM of 16, 36 and 48 is
144

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 16 = 9, 144 ÷ 36 = 4, 144 ÷ 48 = 3 — and 9, 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/16 by 9 and of y/36 by 4 and of z/48 by 3.

16 = 24

36 = 22 × 32

48 = 24 × 3

Prime163648Highest power
224222424
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
1633361,584
1634362,448
1635365,040
163636144
1636375,328
1636382,736
1636391,872
163640720
1636415,904
1636421,008
1636436,192
1636441,584
163645720
1636463,312
1636476,768
163648144
1636497,056
1636503,600
1636512,448
1636521,872
1636537,632
163654432
1636557,920
1636561,008
1636572,736
1636584,176
1636598,496
163660720
1636618,784
1636624,464

FAQ

What's the Least Common Multiple (LCM) of 16, 36 and 48?

LCM of 16, 36 and 48 is 144

How to find the LCM of 16, 36 and 48 by prime factorization?

Take every prime that appears in 16, 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 16, 36 and 48 two numbers at a time?

Yes. The LCM of 16 and 36 is 144, and the LCM of 144 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 16, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 16, 144 ÷ 36 and 144 ÷ 48 all come out whole. Any other common multiple of 16, 36 and 48 is a multiple of 144.

See Also