LCM for 7, 14 and 16

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What's the Least Common Multiple (LCM) of 7, 14 and 16?

Answer

LCM of 7, 14 and 16 is
112

First common multiples: 112, 224, 336, …

112 is divisible by all three: 112 ÷ 7 = 16, 112 ÷ 14 = 8, 112 ÷ 16 = 7 — and 16, 8 and 7 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/7 by 16 and of y/14 by 8 and of z/16 by 7.

7 — prime

14 = 2 × 7

16 = 24

Prime71416Highest power
2—22424
777—7

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

LCM = 24 × 7 = 112

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LCM Table

1st2nd3rdLCM
171414
271414
371442
471428
571470
671442
771414
781456
7914126
7101470
71114154
7121484
71314182
7141414
71415210
71416112
71417238
71418126
71419266
71420140
7142142
71422154
71423322
71424168
71425350
71426182
71427378
7142828
71429406
71430210

FAQ

What's the Least Common Multiple (LCM) of 7, 14 and 16?

LCM of 7, 14 and 16 is 112

How to find the LCM of 7, 14 and 16 by prime factorization?

Take every prime that appears in 7, 14 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 7 = 112.

Can you get the LCM of 7, 14 and 16 two numbers at a time?

Yes. The LCM of 7 and 14 is 14, and the LCM of 14 and 16 is 112 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 112 divisible by 7, 14 and 16?

Yes, and by definition it is the smallest positive integer that is: 112 ÷ 7, 112 ÷ 14 and 112 ÷ 16 all come out whole. Any other common multiple of 7, 14 and 16 is a multiple of 112.

See Also