LCM for 3, 3 and 5

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

What's the Least Common Multiple (LCM) of 3, 3 and 5?

Answer

LCM of 3, 3 and 5 is
15

(Fifteen)

15 is the smallest positive integer that 3, 3 and 5 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 3 and 5 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 3: 3 (exponent form: 3)

All Prime Factors of 3: 3 (exponent form: 3)

All Prime Factors of 5: 5 (exponent form: 5)

Prime factor335Highest power
333—3
5——55

LCM = 3 × 5 = 15

Checking the LCM of 3, 3 and 5 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(3, 3) = (3 × 3) ÷ 3 = 9 ÷ 3 = 3

LCM(3, 5) = (3 × 5) ÷ 1 = 15 ÷ 1 = 15

LCM(3, 3, 5) = 15

The pairs may be taken in any order — 3 and 5 first, then 3 — and the answer is the same 15. That is exactly why the two routes on this page agree.

Related Calculations

See Also

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 3, 3 and 5? (The answer is: 15). Enter the first number (e.g. '3'), the second (e.g. '3') and the third (e.g. '5'), 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
1333
2336
3333
33412
33515
3366
33721
33824
3399
331030
331133
331212
331339
331442
331515
331648
331751
331818
331957
332060
332121
332266
332369
332424
332575
332678
332727
332884
332987
333030

FAQ

What's the Least Common Multiple (LCM) of 3, 3 and 5?

LCM of 3, 3 and 5 is 15

How to find the LCM of 3, 3 and 5 by prime factorization?

Take every prime that appears in 3, 3 and 5 to the highest power it reaches in any one of them and multiply: 3 × 5 = 15.

Can you get the LCM of 3, 3 and 5 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 3 is 3, and the LCM of 3 and 5 is 15 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 15 divisible by 3, 3 and 5?

Yes, and by definition it is the smallest positive integer that is: 15 ÷ 3, 15 ÷ 3 and 15 ÷ 5 all come out whole. Any other common multiple of 3, 3 and 5 is a multiple of 15.

See Also