LCM for 50, 100 and 500

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

What's the Least Common Multiple (LCM) of 50, 100 and 500?

Answer

LCM of 50, 100 and 500 is
500

(Five hundred)

500 is the smallest positive integer that 50, 100 and 500 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 50, 100 and 500 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

All Prime Factors of 500: 2 × 2 × 5 × 5 × 5 (exponent form: 22 × 53)

Prime factor50100500Highest power
22222222
552525353

LCM = 22 × 53 = 500

Checking the LCM of 50, 100 and 500 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(50, 100) = (50 × 100) ÷ 50 = 5,000 ÷ 50 = 100

LCM(100, 500) = (100 × 500) ÷ 100 = 50,000 ÷ 100 = 500

LCM(50, 100, 500) = 500

The pairs may be taken in any order — 100 and 500 first, then 50 — and the answer is the same 500. That is exactly why the two routes on this page agree.

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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 50, 100 and 500? (The answer is: 500). Enter the first number (e.g. '50'), the second (e.g. '100') and the third (e.g. '500'), 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
501004859,700
5010048624,300
5010048748,700
5010048812,200
5010048948,900
501004904,900
5010049149,100
5010049212,300
5010049349,300
5010049424,700
501004959,900
5010049612,400
5010049749,700
5010049824,900
5010049949,900
50100500500
5010050150,100
5010050225,100
5010050350,300
5010050412,600
5010050510,100
5010050625,300
5010050750,700
5010050812,700
5010050950,900
501005105,100
5010051151,100
5010051212,800
5010051351,300
5010051425,700

FAQ

What's the Least Common Multiple (LCM) of 50, 100 and 500?

LCM of 50, 100 and 500 is 500

How to find the LCM of 50, 100 and 500 by prime factorization?

Take every prime that appears in 50, 100 and 500 to the highest power it reaches in any one of them and multiply: 2² × 5³ = 500.

Can you get the LCM of 50, 100 and 500 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 50 and 100 is 100, and the LCM of 100 and 500 is 500 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 500 divisible by 50, 100 and 500?

Yes, and by definition it is the smallest positive integer that is: 500 ÷ 50, 500 ÷ 100 and 500 ÷ 500 all come out whole. Any other common multiple of 50, 100 and 500 is a multiple of 500.

See Also