LCM for 8, 30 and 45

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

What's the Least Common Multiple (LCM) of 8, 30 and 45?

Answer

LCM of 8, 30 and 45 is
360

(Three hundred sixty)

360 is the smallest positive integer that 8, 30 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 30 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

Prime factor83045Highest power
2232—23
3—33232
5—555

LCM = 23 × 32 × 5 = 360

Checking the LCM of 8, 30 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(8, 30) = (8 × 30) ÷ 2 = 240 ÷ 2 = 120

LCM(120, 45) = (120 × 45) ÷ 15 = 5,400 ÷ 15 = 360

LCM(8, 30, 45) = 360

The pairs may be taken in any order — 30 and 45 first, then 8 — and the answer is the same 360. 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 8, 30 and 45? (The answer is: 360). Enter the first number (e.g. '8'), the second (e.g. '30') 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
83030120
830313,720
83032480
830331,320
830342,040
83035840
83036360
830374,440
830382,280
830391,560
83040120
830414,920
83042840
830435,160
830441,320
83045360
830462,760
830475,640
83048240
830495,880
83050600
830512,040
830521,560
830536,360
830541,080
830551,320
83056840
830572,280
830583,480
830597,080

FAQ

What's the Least Common Multiple (LCM) of 8, 30 and 45?

LCM of 8, 30 and 45 is 360

How to find the LCM of 8, 30 and 45 by prime factorization?

Take every prime that appears in 8, 30 and 45 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 8, 30 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 30 is 120, and the LCM of 120 and 45 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 8, 30 and 45?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 30 and 360 ÷ 45 all come out whole. Any other common multiple of 8, 30 and 45 is a multiple of 360.

See Also