LCM for 20, 30 and 50

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 20, 30 and 50?

Answer

LCM of 20, 30 and 50 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 20 = 15, 300 ÷ 30 = 10, 300 ÷ 50 = 6 — and 15, 10 and 6 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/30 by 10 and of z/50 by 6.

20 = 22 × 5

30 = 2 × 3 × 5

50 = 2 × 52

Prime203050Highest power
2222222
3—3—3
5555252

— = 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
203035420
203036180
2030372,220
2030381,140
203039780
203040120
2030412,460
203042420
2030432,580
203044660
203045180
2030461,380
2030472,820
203048240
2030492,940
203050300
2030511,020
203052780
2030533,180
203054540
203055660
203056840
2030571,140
2030581,740
2030593,540
20306060
2030613,660
2030621,860
2030631,260
203064960

FAQ

What's the Least Common Multiple (LCM) of 20, 30 and 50?

LCM of 20, 30 and 50 is 300

How to find the LCM of 20, 30 and 50 by prime factorization?

Take every prime that appears in 20, 30 and 50 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 20, 30 and 50 two numbers at a time?

Yes. The LCM of 20 and 30 is 60, and the LCM of 60 and 50 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, 30 and 50?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 30 and 300 ÷ 50 all come out whole. Any other common multiple of 20, 30 and 50 is a multiple of 300.

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