LCM for 39, 45 and 54

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

What's the Least Common Multiple (LCM) of 39, 45 and 54?

Answer

LCM of 39, 45 and 54 is
3,510

(Three thousand five hundred ten)

3,510 is the smallest positive integer that 39, 45 and 54 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 39, 45 and 54 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 39: 3 × 13 (exponent form: 3 × 13)

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

All Prime Factors of 54: 2 × 3 × 3 × 3 (exponent form: 2 × 33)

Prime factor394554Highest power
2——22
33323333
5—5—5
1313——13

LCM = 2 × 33 × 5 × 13 = 3,510

Checking the LCM of 39, 45 and 54 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(39, 45) = (39 × 45) ÷ 3 = 1,755 ÷ 3 = 585

LCM(585, 54) = (585 × 54) ÷ 9 = 31,590 ÷ 9 = 3,510

LCM(39, 45, 54) = 3,510

The pairs may be taken in any order — 45 and 54 first, then 39 — and the answer is the same 3,510. 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 39, 45 and 54? (The answer is: 3,510). Enter the first number (e.g. '39'), the second (e.g. '45') and the third (e.g. '54'), 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
393945585
3940454,680
39414523,985
3942458,190
39434525,155
39444525,740
394545585
39454626,910
39454727,495
3945489,360
39454928,665
3945505,850
3945519,945
3945522,340
39455331,005
3945543,510
3945556,435
39455632,760
39455711,115
39455833,930
39455934,515
3945602,340
39456135,685
39456236,270
3945634,095
39456437,440
394565585
39456612,870
39456739,195
39456839,780

FAQ

What's the Least Common Multiple (LCM) of 39, 45 and 54?

LCM of 39, 45 and 54 is 3,510

How to find the LCM of 39, 45 and 54 by prime factorization?

Take every prime that appears in 39, 45 and 54 to the highest power it reaches in any one of them and multiply: 2 × 3³ × 5 × 13 = 3,510.

Can you get the LCM of 39, 45 and 54 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 39 and 45 is 585, and the LCM of 585 and 54 is 3,510 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 3,510 divisible by 39, 45 and 54?

Yes, and by definition it is the smallest positive integer that is: 3,510 ÷ 39, 3,510 ÷ 45 and 3,510 ÷ 54 all come out whole. Any other common multiple of 39, 45 and 54 is a multiple of 3,510.

See Also