LCM for 20, 25 and 40

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

What's the Least Common Multiple (LCM) of 20, 25 and 40?

Answer

LCM of 20, 25 and 40 is
200

(Two hundred)

200 is the smallest positive integer that 20, 25 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 25 and 40 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

Prime factor202540Highest power
222—2323
5552552

LCM = 23 × 52 = 200

Checking the LCM of 20, 25 and 40 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, 40) = (100 × 40) ÷ 20 = 4,000 ÷ 20 = 200

LCM(20, 25, 40) = 200

The pairs may be taken in any order — 25 and 40 first, then 20 — and the answer is the same 200. 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 40? (The answer is: 200). Enter the first number (e.g. '20'), the second (e.g. '25') and the third (e.g. '40'), 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
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
202545900
2025462,300
2025474,700
2025481,200
2025494,900
202550100
2025515,100
2025521,300
2025535,300
2025542,700

FAQ

What's the Least Common Multiple (LCM) of 20, 25 and 40?

LCM of 20, 25 and 40 is 200

How to find the LCM of 20, 25 and 40 by prime factorization?

Take every prime that appears in 20, 25 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 5² = 200.

Can you get the LCM of 20, 25 and 40 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 40 is 200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 200 divisible by 20, 25 and 40?

Yes, and by definition it is the smallest positive integer that is: 200 ÷ 20, 200 ÷ 25 and 200 ÷ 40 all come out whole. Any other common multiple of 20, 25 and 40 is a multiple of 200.

See Also