LCM for 10, 15 and 45

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

What's the Least Common Multiple (LCM) of 10, 15 and 45?

Answer

LCM of 10, 15 and 45 is
90

(Ninety)

90 is the smallest positive integer that 10, 15 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 15 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

Prime factor101545Highest power
22——2
3—33232
55555

LCM = 2 × 32 × 5 = 90

Checking the LCM of 10, 15 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(10, 15) = (10 × 15) ÷ 5 = 150 ÷ 5 = 30

LCM(30, 45) = (30 × 45) ÷ 15 = 1,350 ÷ 15 = 90

LCM(10, 15, 45) = 90

The pairs may be taken in any order — 15 and 45 first, then 10 — and the answer is the same 90. That is exactly why the two routes on this page agree.

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See Also

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 10, 15 and 45? (The answer is: 90). Enter the first number (e.g. '10'), the second (e.g. '15') 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
10153030
101531930
101532480
101533330
101534510
101535210
101536180
1015371,110
101538570
101539390
101540120
1015411,230
101542210
1015431,290
101544660
10154590
101546690
1015471,410
101548240
1015491,470
101550150
101551510
101552780
1015531,590
101554270
101555330
101556840
101557570
101558870
1015591,770

FAQ

What's the Least Common Multiple (LCM) of 10, 15 and 45?

LCM of 10, 15 and 45 is 90

How to find the LCM of 10, 15 and 45 by prime factorization?

Take every prime that appears in 10, 15 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 10, 15 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 15 is 30, and the LCM of 30 and 45 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 10, 15 and 45?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 10, 90 ÷ 15 and 90 ÷ 45 all come out whole. Any other common multiple of 10, 15 and 45 is a multiple of 90.

See Also