LCM for 20, 50 and 60

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What's the Least Common Multiple (LCM) of 20, 50 and 60?

Answer

LCM of 20, 50 and 60 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 20 = 15, 300 ÷ 50 = 6, 300 ÷ 60 = 5 — and 15, 6 and 5 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/20 by 15 and of y/50 by 6 and of z/60 by 5.

20 = 22 × 5

50 = 2 × 52

60 = 22 × 3 × 5

Prime205060Highest power
22222222
3——33
5552552

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

LCM = 22 × 3 × 52 = 300

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LCM Table

1st2nd3rdLCM
204550900
2046502,300
2047504,700
2048501,200
2049504,900
205050100
2050515,100
2050521,300
2050535,300
2050542,700
2050551,100
2050561,400
2050575,700
2050582,900
2050595,900
205060300
2050616,100
2050623,100
2050636,300
2050641,600
2050651,300
2050663,300
2050676,700
2050681,700
2050696,900
205070700
2050717,100
2050721,800
2050737,300
2050743,700

FAQ

What's the Least Common Multiple (LCM) of 20, 50 and 60?

LCM of 20, 50 and 60 is 300

How to find the LCM of 20, 50 and 60 by prime factorization?

Take every prime that appears in 20, 50 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 20, 50 and 60 two numbers at a time?

Yes. The LCM of 20 and 50 is 100, and the LCM of 100 and 60 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 300 divisible by 20, 50 and 60?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 50 and 300 ÷ 60 all come out whole. Any other common multiple of 20, 50 and 60 is a multiple of 300.

See Also