LCM for 6, 15 and 40

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

What's the Least Common Multiple (LCM) of 6, 15 and 40?

Answer

LCM of 6, 15 and 40 is
120

(One hundred twenty)

120 is the smallest positive integer that 6, 15 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 15 and 40 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 6: 2 × 3 (exponent form: 2 × 3)

All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

Prime factor61540Highest power
22—2323
333—3
5—555

LCM = 23 × 3 × 5 = 120

Checking the LCM of 6, 15 and 40 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(6, 15) = (6 × 15) ÷ 3 = 90 ÷ 3 = 30

LCM(30, 40) = (30 × 40) ÷ 10 = 1,200 ÷ 10 = 120

LCM(6, 15, 40) = 120

The pairs may be taken in any order — 15 and 40 first, then 6 — and the answer is the same 120. 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 6, 15 and 40? (The answer is: 120). Enter the first number (e.g. '6'), the second (e.g. '15') and the third (e.g. '40'), 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
61525150
61526390
61527270
61528420
61529870
6153030
61531930
61532480
61533330
61534510
61535210
61536180
615371,110
61538570
61539390
61540120
615411,230
61542210
615431,290
61544660
6154590
61546690
615471,410
61548240
615491,470
61550150
61551510
61552780
615531,590
61554270

FAQ

What's the Least Common Multiple (LCM) of 6, 15 and 40?

LCM of 6, 15 and 40 is 120

How to find the LCM of 6, 15 and 40 by prime factorization?

Take every prime that appears in 6, 15 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 6, 15 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 15 is 30, and the LCM of 30 and 40 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 6, 15 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 6, 120 ÷ 15 and 120 ÷ 40 all come out whole. Any other common multiple of 6, 15 and 40 is a multiple of 120.

See Also