LCM for 16, 24 and 48

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What's the Least Common Multiple (LCM) of 16, 24 and 48?

Answer

LCM of 16, 24 and 48 is
48

First common multiples: 48, 96, 144, …

48 is divisible by all three: 48 ÷ 16 = 3, 48 ÷ 24 = 2, 48 ÷ 48 = 1 — and 3, 2 and 1 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 3 and of y/24 by 2.

16 = 24

24 = 23 × 3

48 = 24 × 3

Prime162448Highest power
224232424
3—333

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

LCM = 24 × 3 = 48

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LCM Table

1st2nd3rdLCM
162433528
162434816
1624351,680
162436144
1624371,776
162438912
162439624
162440240
1624411,968
162442336
1624432,064
162444528
162445720
1624461,104
1624472,256
16244848
1624492,352
1624501,200
162451816
162452624
1624532,544
162454432
1624552,640
162456336
162457912
1624581,392
1624592,832
162460240
1624612,928
1624621,488

FAQ

What's the Least Common Multiple (LCM) of 16, 24 and 48?

LCM of 16, 24 and 48 is 48

How to find the LCM of 16, 24 and 48 by prime factorization?

Take every prime that appears in 16, 24 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

Can you get the LCM of 16, 24 and 48 two numbers at a time?

Yes. The LCM of 16 and 24 is 48, and the LCM of 48 and 48 is 48 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 48 divisible by 16, 24 and 48?

Yes, and by definition it is the smallest positive integer that is: 48 ÷ 16, 48 ÷ 24 and 48 ÷ 48 all come out whole. Any other common multiple of 16, 24 and 48 is a multiple of 48.

See Also