LCM for 45, 50 and 60

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What's the Least Common Multiple (LCM) of 45, 50 and 60?

Answer

LCM of 45, 50 and 60 is
900

First common multiples: 900; 1,800; 2,700; …

900 is divisible by all three: 900 ÷ 45 = 20, 900 ÷ 50 = 18, 900 ÷ 60 = 15 — and 20, 18 and 15 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/45 by 20 and of y/50 by 18 and of z/60 by 15.

45 = 32 × 5

50 = 2 × 52

60 = 22 × 3 × 5

Prime455060Highest power
2—22222
332—332
5552552

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

LCM = 22 × 32 × 52 = 900

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LCM Table

1st2nd3rdLCM
454550450
45465010,350
45475021,150
4548503,600
45495022,050
455050450
4550517,650
45505211,700
45505323,850
4550541,350
4550554,950
45505612,600
4550578,550
45505813,050
45505926,550
455060900
45506127,450
45506213,950
4550633,150
45506414,400
4550655,850
4550664,950
45506730,150
45506815,300
45506910,350
4550703,150
45507131,950
4550721,800
45507332,850
45507416,650

FAQ

What's the Least Common Multiple (LCM) of 45, 50 and 60?

LCM of 45, 50 and 60 is 900

How to find the LCM of 45, 50 and 60 by prime factorization?

Take every prime that appears in 45, 50 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5² = 900.

Can you get the LCM of 45, 50 and 60 two numbers at a time?

Yes. The LCM of 45 and 50 is 450, and the LCM of 450 and 60 is 900 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 900 divisible by 45, 50 and 60?

Yes, and by definition it is the smallest positive integer that is: 900 ÷ 45, 900 ÷ 50 and 900 ÷ 60 all come out whole. Any other common multiple of 45, 50 and 60 is a multiple of 900.

See Also