LCM for 20, 24 and 45

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 20, 24 and 45?

Answer

LCM of 20, 24 and 45 is
360

(Three hundred sixty)

360 is the smallest positive integer that 20, 24 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 24 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

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

Prime factor202445Highest power
22223—23
3—33232
55—55

LCM = 23 × 32 × 5 = 360

Checking the LCM of 20, 24 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(20, 24) = (20 × 24) ÷ 4 = 480 ÷ 4 = 120

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

LCM(20, 24, 45) = 360

The pairs may be taken in any order — 24 and 45 first, then 20 — 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 20, 24 and 45? (The answer is: 360). Enter the first number (e.g. '20'), the second (e.g. '24') 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
202430120
2024313,720
202432480
2024331,320
2024342,040
202435840
202436360
2024374,440
2024382,280
2024391,560
202440120
2024414,920
202442840
2024435,160
2024441,320
202445360
2024462,760
2024475,640
202448240
2024495,880
202450600
2024512,040
2024521,560
2024536,360
2024541,080
2024551,320
202456840
2024572,280
2024583,480
2024597,080

FAQ

What's the Least Common Multiple (LCM) of 20, 24 and 45?

LCM of 20, 24 and 45 is 360

How to find the LCM of 20, 24 and 45 by prime factorization?

Take every prime that appears in 20, 24 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 20, 24 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 20 and 24 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 20, 24 and 45?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 20, 360 ÷ 24 and 360 ÷ 45 all come out whole. Any other common multiple of 20, 24 and 45 is a multiple of 360.

See Also