LCM for 45, 50 and 60

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 45, 50 and 60?

Answer

LCM of 45, 50 and 60 is
900

(Nine hundred)

900 is the smallest positive integer that 45, 50 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 45, 50 and 60 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

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

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

Prime factor455060Highest power
2—22222
332—332
5552552

LCM = 22 × 32 × 52 = 900

Checking the LCM of 45, 50 and 60 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(45, 50) = (45 × 50) ÷ 5 = 2,250 ÷ 5 = 450

LCM(450, 60) = (450 × 60) ÷ 30 = 27,000 ÷ 30 = 900

LCM(45, 50, 60) = 900

The pairs may be taken in any order — 50 and 60 first, then 45 — and the answer is the same 900. That is exactly why the two routes on this page agree.

Related Calculations

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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 45, 50 and 60? (The answer is: 900). Enter the first number (e.g. '45'), the second (e.g. '50') and the third (e.g. '60'), 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
454550450
45465010,350
45475021,150
4548503,600
45495022,050
455050450
4550517,650
45505211,700
45505323,850
4550541,350
4550554,950
45505612,600
4550578,550
45505813,050
45505926,550
455060900
45506127,450
45506213,950
4550633,150
45506414,400
4550655,850
4550664,950
45506730,150
45506815,300
45506910,350
4550703,150
45507131,950
4550721,800
45507332,850
45507416,650

FAQ

What's the Least Common Multiple (LCM) of 45, 50 and 60?

LCM of 45, 50 and 60 is 900

How to find the LCM of 45, 50 and 60 by prime factorization?

Take every prime that appears in 45, 50 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5² = 900.

Can you get the LCM of 45, 50 and 60 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 45 and 50 is 450, and the LCM of 450 and 60 is 900 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 900 divisible by 45, 50 and 60?

Yes, and by definition it is the smallest positive integer that is: 900 ÷ 45, 900 ÷ 50 and 900 ÷ 60 all come out whole. Any other common multiple of 45, 50 and 60 is a multiple of 900.

See Also