LCM for 10, 25 and 50

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

What's the Least Common Multiple (LCM) of 10, 25 and 50?

Answer

LCM of 10, 25 and 50 is
50

(Fifty)

50 is the smallest positive integer that 10, 25 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 25 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

Prime factor102550Highest power
22—22
55525252

LCM = 2 × 52 = 50

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

LCM(50, 50) = (50 × 50) ÷ 50 = 2,500 ÷ 50 = 50

LCM(10, 25, 50) = 50

The pairs may be taken in any order — 25 and 50 first, then 10 — and the answer is the same 50. 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 10, 25 and 50? (The answer is: 50). Enter the first number (e.g. '10'), the second (e.g. '25') 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
102535350
102536900
1025371,850
102538950
1025391,950
102540200
1025412,050
1025421,050
1025432,150
1025441,100
102545450
1025461,150
1025472,350
1025481,200
1025492,450
10255050
1025512,550
1025521,300
1025532,650
1025541,350
102555550
1025561,400
1025572,850
1025581,450
1025592,950
102560300
1025613,050
1025621,550
1025633,150
1025641,600

FAQ

What's the Least Common Multiple (LCM) of 10, 25 and 50?

LCM of 10, 25 and 50 is 50

How to find the LCM of 10, 25 and 50 by prime factorization?

Take every prime that appears in 10, 25 and 50 to the highest power it reaches in any one of them and multiply: 2 × 5² = 50.

Can you get the LCM of 10, 25 and 50 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 50 is 50 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 50 divisible by 10, 25 and 50?

Yes, and by definition it is the smallest positive integer that is: 50 ÷ 10, 50 ÷ 25 and 50 ÷ 50 all come out whole. Any other common multiple of 10, 25 and 50 is a multiple of 50.

See Also