LCM for 16, 18 and 45

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

What's the Least Common Multiple (LCM) of 16, 18 and 45?

Answer

LCM of 16, 18 and 45 is
720

(Seven hundred twenty)

720 is the smallest positive integer that 16, 18 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

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

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

Prime factor161845Highest power
2242—24
3—323232
5——55

LCM = 24 × 32 × 5 = 720

Checking the LCM of 16, 18 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(16, 18) = (16 × 18) ÷ 2 = 288 ÷ 2 = 144

LCM(144, 45) = (144 × 45) ÷ 9 = 6,480 ÷ 9 = 720

LCM(16, 18, 45) = 720

The pairs may be taken in any order — 18 and 45 first, then 16 — and the answer is the same 720. That is exactly why the two routes on this page agree.

Related Calculations

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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 16, 18 and 45? (The answer is: 720). Enter the first number (e.g. '16'), the second (e.g. '18') 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
161830720
1618314,464
161832288
1618331,584
1618342,448
1618355,040
161836144
1618375,328
1618382,736
1618391,872
161840720
1618415,904
1618421,008
1618436,192
1618441,584
161845720
1618463,312
1618476,768
161848144
1618497,056
1618503,600
1618512,448
1618521,872
1618537,632
161854432
1618557,920
1618561,008
1618572,736
1618584,176
1618598,496

FAQ

What's the Least Common Multiple (LCM) of 16, 18 and 45?

LCM of 16, 18 and 45 is 720

How to find the LCM of 16, 18 and 45 by prime factorization?

Take every prime that appears in 16, 18 and 45 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

Can you get the LCM of 16, 18 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 18 is 144, and the LCM of 144 and 45 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 16, 18 and 45?

Yes, and by definition it is the smallest positive integer that is: 720 ÷ 16, 720 ÷ 18 and 720 ÷ 45 all come out whole. Any other common multiple of 16, 18 and 45 is a multiple of 720.

See Also