LCM for 16, 32 and 48

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What's the Least Common Multiple (LCM) of 16, 32 and 48?

Answer

LCM of 16, 32 and 48 is
96

First common multiples: 96, 192, 288, …

96 is divisible by all three: 96 ÷ 16 = 6, 96 ÷ 32 = 3, 96 ÷ 48 = 2 — and 6, 3 and 2 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 6 and of y/32 by 3 and of z/48 by 2.

16 = 24

32 = 25

48 = 24 × 3

Prime163248Highest power
224252425
3——33

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

LCM = 25 × 3 = 96

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LCM Table

1st2nd3rdLCM
1632331,056
163234544
1632351,120
163236288
1632371,184
163238608
1632391,248
163240160
1632411,312
163242672
1632431,376
163244352
1632451,440
163246736
1632471,504
16324896
1632491,568
163250800
1632511,632
163252416
1632531,696
163254864
1632551,760
163256224
1632571,824
163258928
1632591,888
163260480
1632611,952
163262992

FAQ

What's the Least Common Multiple (LCM) of 16, 32 and 48?

LCM of 16, 32 and 48 is 96

How to find the LCM of 16, 32 and 48 by prime factorization?

Take every prime that appears in 16, 32 and 48 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 = 96.

Can you get the LCM of 16, 32 and 48 two numbers at a time?

Yes. The LCM of 16 and 32 is 32, and the LCM of 32 and 48 is 96 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 96 divisible by 16, 32 and 48?

Yes, and by definition it is the smallest positive integer that is: 96 ÷ 16, 96 ÷ 32 and 96 ÷ 48 all come out whole. Any other common multiple of 16, 32 and 48 is a multiple of 96.

See Also