LCM for 15, 27 and 45

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 15, 27 and 45?

Answer

LCM of 15, 27 and 45 is
135

(One hundred thirty-five)

135 is the smallest positive integer that 15, 27 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 27 and 45 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 27: 3 × 3 × 3 (exponent form: 33)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor152745Highest power
33333233
55—55

LCM = 33 × 5 = 135

Checking the LCM of 15, 27 and 45 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(15, 27) = (15 × 27) ÷ 3 = 405 ÷ 3 = 135

LCM(135, 45) = (135 × 45) ÷ 45 = 6,075 ÷ 45 = 135

LCM(15, 27, 45) = 135

The pairs may be taken in any order — 27 and 45 first, then 15 — and the answer is the same 135. 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 15, 27 and 45? (The answer is: 135). Enter the first number (e.g. '15'), the second (e.g. '27') and the third (e.g. '45'), 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
152730270
1527314,185
1527324,320
1527331,485
1527344,590
152735945
152736540
1527374,995
1527385,130
1527391,755
1527401,080
1527415,535
1527421,890
1527435,805
1527445,940
152745135
1527466,210
1527476,345
1527482,160
1527496,615
1527501,350
1527512,295
1527527,020
1527537,155
152754270
1527551,485
1527567,560
1527572,565
1527587,830
1527597,965

FAQ

What's the Least Common Multiple (LCM) of 15, 27 and 45?

LCM of 15, 27 and 45 is 135

How to find the LCM of 15, 27 and 45 by prime factorization?

Take every prime that appears in 15, 27 and 45 to the highest power it reaches in any one of them and multiply: 3³ × 5 = 135.

Can you get the LCM of 15, 27 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 27 is 135, and the LCM of 135 and 45 is 135 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 135 divisible by 15, 27 and 45?

Yes, and by definition it is the smallest positive integer that is: 135 ÷ 15, 135 ÷ 27 and 135 ÷ 45 all come out whole. Any other common multiple of 15, 27 and 45 is a multiple of 135.

See Also