LCM for 45, 120 and 525

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

What's the Least Common Multiple (LCM) of 45, 120 and 525?

Answer

LCM of 45, 120 and 525 is
12,600

(Twelve thousand six hundred)

12,600 is the smallest positive integer that 45, 120 and 525 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 45, 120 and 525 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

All Prime Factors of 525: 3 × 5 × 5 × 7 (exponent form: 3 × 52 × 7)

Prime factor45120525Highest power
2—23—23
3323332
5555252
7——77

LCM = 23 × 32 × 52 × 7 = 12,600

Checking the LCM of 45, 120 and 525 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(45, 120) = (45 × 120) ÷ 15 = 5,400 ÷ 15 = 360

LCM(360, 525) = (360 × 525) ÷ 15 = 189,000 ÷ 15 = 12,600

LCM(45, 120, 525) = 12,600

The pairs may be taken in any order — 120 and 525 first, then 45 — and the answer is the same 12,600. 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 45, 120 and 525? (The answer is: 12,600). Enter the first number (e.g. '45'), the second (e.g. '120') and the third (e.g. '525'), 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
451205106,120
45120511183,960
4512051223,040
4512051320,520
4512051492,520
4512051537,080
4512051615,480
45120517186,120
4512051893,240
4512051962,280
451205204,680
45120521187,560
4512052210,440
45120523188,280
4512052447,160
4512052512,600
4512052694,680
45120527189,720
451205287,920
45120529190,440
4512053019,080
4512053121,240
4512053247,880
45120533191,880
4512053432,040
4512053538,520
4512053624,120
4512053764,440
4512053896,840
45120539194,040

FAQ

What's the Least Common Multiple (LCM) of 45, 120 and 525?

LCM of 45, 120 and 525 is 12,600

How to find the LCM of 45, 120 and 525 by prime factorization?

Take every prime that appears in 45, 120 and 525 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5² × 7 = 12,600.

Can you get the LCM of 45, 120 and 525 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 45 and 120 is 360, and the LCM of 360 and 525 is 12,600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 12,600 divisible by 45, 120 and 525?

Yes, and by definition it is the smallest positive integer that is: 12,600 ÷ 45, 12,600 ÷ 120 and 12,600 ÷ 525 all come out whole. Any other common multiple of 45, 120 and 525 is a multiple of 12,600.

See Also