LCM for 10, 16 and 18

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

What's the Least Common Multiple (LCM) of 10, 16 and 18?

Answer

LCM of 10, 16 and 18 is
720

(Seven hundred twenty)

720 is the smallest positive integer that 10, 16 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 16 and 18 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

Prime factor101618Highest power
2224224
3——3232
55——5

LCM = 24 × 32 × 5 = 720

Checking the LCM of 10, 16 and 18 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, 16) = (10 × 16) ÷ 2 = 160 ÷ 2 = 80

LCM(80, 18) = (80 × 18) ÷ 2 = 1,440 ÷ 2 = 720

LCM(10, 16, 18) = 720

The pairs may be taken in any order — 16 and 18 first, then 10 — and the answer is the same 720. 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, 16 and 18? (The answer is: 720). Enter the first number (e.g. '10'), the second (e.g. '16') and the third (e.g. '18'), 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
31016240
4101680
5101680
61016240
71016560
8101680
91016720
10101680
101116880
101216240
1013161,040
101416560
101516240
10161680
1016171,360
101618720
1016191,520
10162080
1016211,680
101622880
1016231,840
101624240
101625400
1016261,040
1016272,160
101628560
1016292,320
101630240
1016312,480
101632160

FAQ

What's the Least Common Multiple (LCM) of 10, 16 and 18?

LCM of 10, 16 and 18 is 720

How to find the LCM of 10, 16 and 18 by prime factorization?

Take every prime that appears in 10, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

Can you get the LCM of 10, 16 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 16 is 80, and the LCM of 80 and 18 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 720 divisible by 10, 16 and 18?

Yes, and by definition it is the smallest positive integer that is: 720 ÷ 10, 720 ÷ 16 and 720 ÷ 18 all come out whole. Any other common multiple of 10, 16 and 18 is a multiple of 720.

See Also