LCM for 20, 25 and 30

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

What's the Least Common Multiple (LCM) of 20, 25 and 30?

Answer

LCM of 20, 25 and 30 is
300

(Three hundred)

300 is the smallest positive integer that 20, 25 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 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 20: 2 × 2 × 5 (exponent form: 22 × 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 factor202530Highest power
222—222
3——33
5552552

LCM = 22 × 3 × 52 = 300

Checking the LCM of 20, 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(20, 25) = (20 × 25) ÷ 5 = 500 ÷ 5 = 100

LCM(100, 30) = (100 × 30) ÷ 10 = 3,000 ÷ 10 = 300

LCM(20, 25, 30) = 300

The pairs may be taken in any order — 25 and 30 first, then 20 — and the answer is the same 300. 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 20, 25 and 30? (The answer is: 300). Enter the first number (e.g. '20'), 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
152025300
162025400
1720251,700
182025900
1920251,900
202025100
2021252,100
2022251,100
2023252,300
202425600
202525100
2025261,300
2025272,700
202528700
2025292,900
202530300
2025313,100
202532800
2025333,300
2025341,700
202535700
202536900
2025373,700
2025381,900
2025393,900
202540200
2025414,100
2025422,100
2025434,300
2025441,100

FAQ

What's the Least Common Multiple (LCM) of 20, 25 and 30?

LCM of 20, 25 and 30 is 300

How to find the LCM of 20, 25 and 30 by prime factorization?

Take every prime that appears in 20, 25 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 20, 25 and 30 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 20 and 25 is 100, and the LCM of 100 and 30 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 300 divisible by 20, 25 and 30?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 25 and 300 ÷ 30 all come out whole. Any other common multiple of 20, 25 and 30 is a multiple of 300.

See Also