LCM for 8, 14 and 16

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What's the Least Common Multiple (LCM) of 8, 14 and 16?

Answer

LCM of 8, 14 and 16 is
112

First common multiples: 112, 224, 336, …

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

8 = 23

14 = 2 × 7

16 = 24

Prime81416Highest power
22322424
7—7—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
181456
281456
3814168
481456
5814280
6814168
781456
881456
8914504
81014280
81114616
81214168
81314728
8141456
81415840
81416112
81417952
81418504
814191,064
81420280
81421168
81422616
814231,288
81424168
814251,400
81426728
814271,512
8142856
814291,624
81430840

FAQ

What's the Least Common Multiple (LCM) of 8, 14 and 16?

LCM of 8, 14 and 16 is 112

How to find the LCM of 8, 14 and 16 by prime factorization?

Take every prime that appears in 8, 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 8, 14 and 16 two numbers at a time?

Yes. The LCM of 8 and 14 is 56, and the LCM of 56 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 8, 14 and 16?

Yes, and by definition it is the smallest positive integer that is: 112 ÷ 8, 112 ÷ 14 and 112 ÷ 16 all come out whole. Any other common multiple of 8, 14 and 16 is a multiple of 112.

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