LCM for 16, 18 and 45

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What's the Least Common Multiple (LCM) of 16, 18 and 45?

Answer

LCM of 16, 18 and 45 is
720

First common multiples: 720; 1,440; 2,160; …

720 is divisible by all three: 720 ÷ 16 = 45, 720 ÷ 18 = 40, 720 ÷ 45 = 16 — and 45, 40 and 16 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 45 and of y/18 by 40 and of z/45 by 16.

16 = 24

18 = 2 × 32

45 = 32 × 5

Prime161845Highest power
2242—24
3—323232
5——55

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

LCM = 24 × 32 × 5 = 720

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LCM Table

1st2nd3rdLCM
161830720
1618314,464
161832288
1618331,584
1618342,448
1618355,040
161836144
1618375,328
1618382,736
1618391,872
161840720
1618415,904
1618421,008
1618436,192
1618441,584
161845720
1618463,312
1618476,768
161848144
1618497,056
1618503,600
1618512,448
1618521,872
1618537,632
161854432
1618557,920
1618561,008
1618572,736
1618584,176
1618598,496

FAQ

What's the Least Common Multiple (LCM) of 16, 18 and 45?

LCM of 16, 18 and 45 is 720

How to find the LCM of 16, 18 and 45 by prime factorization?

Take every prime that appears in 16, 18 and 45 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

Can you get the LCM of 16, 18 and 45 two numbers at a time?

Yes. The LCM of 16 and 18 is 144, and the LCM of 144 and 45 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 720 divisible by 16, 18 and 45?

Yes, and by definition it is the smallest positive integer that is: 720 ÷ 16, 720 ÷ 18 and 720 ÷ 45 all come out whole. Any other common multiple of 16, 18 and 45 is a multiple of 720.

See Also