LCM for 45, 135 and 225

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 45, 135 and 225?

Answer

LCM of 45, 135 and 225 is
675

(Six hundred seventy-five)

675 is the smallest positive integer that 45, 135 and 225 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 45, 135 and 225 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 135: 3 × 3 × 3 × 5 (exponent form: 33 × 5)

All Prime Factors of 225: 3 × 3 × 5 × 5 (exponent form: 32 × 52)

Prime factor45135225Highest power
332333233
5555252

LCM = 33 × 52 = 675

Checking the LCM of 45, 135 and 225 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, 135) = (45 × 135) ÷ 45 = 6,075 ÷ 45 = 135

LCM(135, 225) = (135 × 225) ÷ 45 = 30,375 ÷ 45 = 675

LCM(45, 135, 225) = 675

The pairs may be taken in any order — 135 and 225 first, then 45 — and the answer is the same 675. 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 45, 135 and 225? (The answer is: 675). Enter the first number (e.g. '45'), the second (e.g. '135') and the third (e.g. '225'), 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
451352101,890
4513521128,485
4513521228,620
451352139,585
4513521428,890
451352155,805
451352161,080
4513521729,295
4513521829,430
451352199,855
451352205,940
4513522129,835
451352229,990
4513522330,105
4513522430,240
45135225675
4513522630,510
4513522730,645
4513522810,260
4513522930,915
451352306,210
4513523110,395
4513523231,320
4513523331,455
451352343,510
451352356,345
4513523631,860
4513523710,665
4513523832,130
4513523932,265

FAQ

What's the Least Common Multiple (LCM) of 45, 135 and 225?

LCM of 45, 135 and 225 is 675

How to find the LCM of 45, 135 and 225 by prime factorization?

Take every prime that appears in 45, 135 and 225 to the highest power it reaches in any one of them and multiply: 3³ × 5² = 675.

Can you get the LCM of 45, 135 and 225 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 45 and 135 is 135, and the LCM of 135 and 225 is 675 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 675 divisible by 45, 135 and 225?

Yes, and by definition it is the smallest positive integer that is: 675 ÷ 45, 675 ÷ 135 and 675 ÷ 225 all come out whole. Any other common multiple of 45, 135 and 225 is a multiple of 675.

See Also