LCM for 10, 25 and 30

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

What's the Least Common Multiple (LCM) of 10, 25 and 30?

Answer

LCM of 10, 25 and 30 is
150

(One hundred fifty)

150 is the smallest positive integer that 10, 25 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 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 10: 2 × 5 (exponent form: 2 × 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 factor102530Highest power
22—22
3——33
5552552

LCM = 2 × 3 × 52 = 150

Checking the LCM of 10, 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(10, 25) = (10 × 25) ÷ 5 = 250 ÷ 5 = 50

LCM(50, 30) = (50 × 30) ÷ 10 = 1,500 ÷ 10 = 150

LCM(10, 25, 30) = 150

The pairs may be taken in any order — 25 and 30 first, then 10 — and the answer is the same 150. 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 10, 25 and 30? (The answer is: 150). Enter the first number (e.g. '10'), 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
101525150
101625400
101725850
101825450
101925950
102025100
1021251,050
102225550
1023251,150
102425600
10252550
102526650
1025271,350
102528700
1025291,450
102530150
1025311,550
102532800
1025331,650
102534850
102535350
102536900
1025371,850
102538950
1025391,950
102540200
1025412,050
1025421,050
1025432,150
1025441,100

FAQ

What's the Least Common Multiple (LCM) of 10, 25 and 30?

LCM of 10, 25 and 30 is 150

How to find the LCM of 10, 25 and 30 by prime factorization?

Take every prime that appears in 10, 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 10, 25 and 30 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 25 is 50, and the LCM of 50 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 10, 25 and 30?

Yes, and by definition it is the smallest positive integer that is: 150 ÷ 10, 150 ÷ 25 and 150 ÷ 30 all come out whole. Any other common multiple of 10, 25 and 30 is a multiple of 150.

See Also