LCM for 20, 50 and 75

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What's the Least Common Multiple (LCM) of 20, 50 and 75?

Answer

LCM of 20, 50 and 75 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 20 = 15, 300 ÷ 50 = 6, 300 ÷ 75 = 4 — and 15, 6 and 4 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/75 by 4.

20 = 22 × 5

50 = 2 × 52

75 = 3 × 52

Prime205075Highest power
2222—22
3——33
55525252

— = 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
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
205075300
2050761,900
2050777,700
2050783,900
2050797,900
205080400
2050818,100
2050824,100
2050838,300
2050842,100
2050851,700
2050864,300
2050878,700
2050882,200
2050898,900

FAQ

What's the Least Common Multiple (LCM) of 20, 50 and 75?

LCM of 20, 50 and 75 is 300

How to find the LCM of 20, 50 and 75 by prime factorization?

Take every prime that appears in 20, 50 and 75 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 75 two numbers at a time?

Yes. The LCM of 20 and 50 is 100, and the LCM of 100 and 75 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 75?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 50 and 300 ÷ 75 all come out whole. Any other common multiple of 20, 50 and 75 is a multiple of 300.

See Also