LCM for 4, 9 and 16

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 4, 9 and 16?

Answer

LCM of 4, 9 and 16 is
144

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 4 = 36, 144 ÷ 9 = 16, 144 ÷ 16 = 9 — and 36, 16 and 9 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/4 by 36 and of y/9 by 16 and of z/16 by 9.

4 = 22

9 = 32

16 = 24

Prime4916Highest power
222—2424
3—32—32

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

LCM = 24 × 32 = 144

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LCM Table

1st2nd3rdLCM
14936
24936
34936
44936
459180
46936
479252
48972
49936
4910180
4911396
491236
4913468
4914252
4915180
4916144
4917612
491836
4919684
4920180
4921252
4922396
4923828
492472
4925900
4926468
4927108
4928252
49291,044
4930180

FAQ

What's the Least Common Multiple (LCM) of 4, 9 and 16?

LCM of 4, 9 and 16 is 144

How to find the LCM of 4, 9 and 16 by prime factorization?

Take every prime that appears in 4, 9 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 4, 9 and 16 two numbers at a time?

Yes. The LCM of 4 and 9 is 36, and the LCM of 36 and 16 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 4, 9 and 16?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 4, 144 ÷ 9 and 144 ÷ 16 all come out whole. Any other common multiple of 4, 9 and 16 is a multiple of 144.

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