LCM for 16, 48 and 64

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What's the Least Common Multiple (LCM) of 16, 48 and 64?

Answer

LCM of 16, 48 and 64 is
192

First common multiples: 192, 384, 576, …

192 is divisible by all three: 192 ÷ 16 = 12, 192 ÷ 48 = 4, 192 ÷ 64 = 3 — and 12, 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 12 and of y/48 by 4 and of z/64 by 3.

16 = 24

48 = 24 × 3

64 = 26

Prime164864Highest power
224242626
3—3—3

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

LCM = 26 × 3 = 192

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LCM Table

1st2nd3rdLCM
1648492,352
1648501,200
164851816
164852624
1648532,544
164854432
1648552,640
164856336
164857912
1648581,392
1648592,832
164860240
1648612,928
1648621,488
1648631,008
164864192
1648653,120
164866528
1648673,216
164868816
1648691,104
1648701,680
1648713,408
164872144
1648733,504
1648741,776
1648751,200
164876912
1648773,696
164878624

FAQ

What's the Least Common Multiple (LCM) of 16, 48 and 64?

LCM of 16, 48 and 64 is 192

How to find the LCM of 16, 48 and 64 by prime factorization?

Take every prime that appears in 16, 48 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 = 192.

Can you get the LCM of 16, 48 and 64 two numbers at a time?

Yes. The LCM of 16 and 48 is 48, and the LCM of 48 and 64 is 192 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 192 divisible by 16, 48 and 64?

Yes, and by definition it is the smallest positive integer that is: 192 ÷ 16, 192 ÷ 48 and 192 ÷ 64 all come out whole. Any other common multiple of 16, 48 and 64 is a multiple of 192.

See Also