LCM for 20, 50 and 75

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

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

Answer

LCM of 20, 50 and 75 is
300

(Three hundred)

300 is the smallest positive integer that 20, 50 and 75 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 50 and 75 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

Prime factor205075Highest power
2222—22
3——33
55525252

LCM = 22 × 3 × 52 = 300

Checking the LCM of 20, 50 and 75 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(20, 50) = (20 × 50) ÷ 10 = 1,000 ÷ 10 = 100

LCM(100, 75) = (100 × 75) ÷ 25 = 7,500 ÷ 25 = 300

LCM(20, 50, 75) = 300

The pairs may be taken in any order — 50 and 75 first, then 20 — and the answer is the same 300. That is exactly why the two routes on this page agree.

Related Calculations

See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 20, 50 and 75? (The answer is: 300). Enter the first number (e.g. '20'), the second (e.g. '50') and the third (e.g. '75'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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