LCM for 12, 16 and 50

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What's the Least Common Multiple (LCM) of 12, 16 and 50?

Answer

LCM of 12, 16 and 50 is
1,200

First common multiples: 1,200; 2,400; 3,600; …

1,200 is divisible by all three: 1,200 ÷ 12 = 100; 1,200 ÷ 16 = 75; 1,200 ÷ 50 = 24 — and 100, 75 and 24 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/12 by 100 and of y/16 by 75 and of z/50 by 24.

12 = 22 × 3

16 = 24

50 = 2 × 52

Prime121650Highest power
22224224
33——3
5——5252

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

LCM = 24 × 3 × 52 = 1,200

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LCM Table

1st2nd3rdLCM
1216351,680
121636144
1216371,776
121638912
121639624
121640240
1216411,968
121642336
1216432,064
121644528
121645720
1216461,104
1216472,256
12164848
1216492,352
1216501,200
121651816
121652624
1216532,544
121654432
1216552,640
121656336
121657912
1216581,392
1216592,832
121660240
1216612,928
1216621,488
1216631,008
121664192

FAQ

What's the Least Common Multiple (LCM) of 12, 16 and 50?

LCM of 12, 16 and 50 is 1,200

How to find the LCM of 12, 16 and 50 by prime factorization?

Take every prime that appears in 12, 16 and 50 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5² = 1,200.

Can you get the LCM of 12, 16 and 50 two numbers at a time?

Yes. The LCM of 12 and 16 is 48, and the LCM of 48 and 50 is 1,200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,200 divisible by 12, 16 and 50?

Yes, and by definition it is the smallest positive integer that is: 1,200 ÷ 12, 1,200 ÷ 16 and 1,200 ÷ 50 all come out whole. Any other common multiple of 12, 16 and 50 is a multiple of 1,200.

See Also