LCM for 5, 25 and 30

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

What's the Least Common Multiple (LCM) of 5, 25 and 30?

Answer

LCM of 5, 25 and 30 is
150

(One hundred fifty)

150 is the smallest positive integer that 5, 25 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 5, 25 and 30 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 5: 5 (exponent form: 5)

All Prime Factors of 25: 5 × 5 (exponent form: 52)

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

Prime factor52530Highest power
2——22
3——33
5552552

LCM = 2 × 3 × 52 = 150

Checking the LCM of 5, 25 and 30 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(5, 25) = (5 × 25) ÷ 5 = 125 ÷ 5 = 25

LCM(25, 30) = (25 × 30) ÷ 5 = 750 ÷ 5 = 150

LCM(5, 25, 30) = 150

The pairs may be taken in any order — 25 and 30 first, then 5 — and the answer is the same 150. That is exactly why the two routes on this page agree.

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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 5, 25 and 30? (The answer is: 150). Enter the first number (e.g. '5'), the second (e.g. '25') and the third (e.g. '30'), 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
5152575
51625400
51725425
51825450
51925475
52025100
52125525
52225550
52325575
52425600
5252525
52526650
52527675
52528700
52529725
52530150
52531775
52532800
52533825
52534850
52535175
52536900
52537925
52538950
52539975
52540200
525411,025
525421,050
525431,075
525441,100

FAQ

What's the Least Common Multiple (LCM) of 5, 25 and 30?

LCM of 5, 25 and 30 is 150

How to find the LCM of 5, 25 and 30 by prime factorization?

Take every prime that appears in 5, 25 and 30 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5² = 150.

Can you get the LCM of 5, 25 and 30 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 5 and 25 is 25, and the LCM of 25 and 30 is 150 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 150 divisible by 5, 25 and 30?

Yes, and by definition it is the smallest positive integer that is: 150 ÷ 5, 150 ÷ 25 and 150 ÷ 30 all come out whole. Any other common multiple of 5, 25 and 30 is a multiple of 150.

See Also