LCM for 20, 40 and 50

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

What's the Least Common Multiple (LCM) of 20, 40 and 50?

Answer

LCM of 20, 40 and 50 is
200

(Two hundred)

200 is the smallest positive integer that 20, 40 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 40 and 50 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

Prime factor204050Highest power
22223223
5555252

LCM = 23 × 52 = 200

Checking the LCM of 20, 40 and 50 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, 40) = (20 × 40) ÷ 20 = 800 ÷ 20 = 40

LCM(40, 50) = (40 × 50) ÷ 10 = 2,000 ÷ 10 = 200

LCM(20, 40, 50) = 200

The pairs may be taken in any order — 40 and 50 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, 40 and 50? (The answer is: 200). Enter the first number (e.g. '20'), the second (e.g. '40') and the third (e.g. '50'), 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
203540280
203640360
2037401,480
203840760
2039401,560
20404040
2040411,640
204042840
2040431,720
204044440
204045360
204046920
2040471,880
204048240
2040491,960
204050200
2040512,040
204052520
2040532,120
2040541,080
204055440
204056280
2040572,280
2040581,160
2040592,360
204060120
2040612,440
2040621,240
2040632,520
204064320

FAQ

What's the Least Common Multiple (LCM) of 20, 40 and 50?

LCM of 20, 40 and 50 is 200

How to find the LCM of 20, 40 and 50 by prime factorization?

Take every prime that appears in 20, 40 and 50 to the highest power it reaches in any one of them and multiply: 2³ × 5² = 200.

Can you get the LCM of 20, 40 and 50 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 20 and 40 is 40, and the LCM of 40 and 50 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, 40 and 50?

Yes, and by definition it is the smallest positive integer that is: 200 ÷ 20, 200 ÷ 40 and 200 ÷ 50 all come out whole. Any other common multiple of 20, 40 and 50 is a multiple of 200.

See Also