LCM for 10, 20 and 50

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

What's the Least Common Multiple (LCM) of 10, 20 and 50?

Answer

LCM of 10, 20 and 50 is
100

(One hundred)

100 is the smallest positive integer that 10, 20 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 20 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

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

Prime factor102050Highest power
2222222
5555252

LCM = 22 × 52 = 100

Checking the LCM of 10, 20 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, 20) = (10 × 20) ÷ 10 = 200 ÷ 10 = 20

LCM(20, 50) = (20 × 50) ÷ 10 = 1,000 ÷ 10 = 100

LCM(10, 20, 50) = 100

The pairs may be taken in any order — 20 and 50 first, then 10 — and the answer is the same 100. 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, 20 and 50? (The answer is: 100). Enter the first number (e.g. '10'), the second (e.g. '20') 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
102035140
102036180
102037740
102038380
102039780
10204040
102041820
102042420
102043860
102044220
102045180
102046460
102047940
102048240
102049980
102050100
1020511,020
102052260
1020531,060
102054540
102055220
102056280
1020571,140
102058580
1020591,180
10206060
1020611,220
102062620
1020631,260
102064320

FAQ

What's the Least Common Multiple (LCM) of 10, 20 and 50?

LCM of 10, 20 and 50 is 100

How to find the LCM of 10, 20 and 50 by prime factorization?

Take every prime that appears in 10, 20 and 50 to the highest power it reaches in any one of them and multiply: 2² × 5² = 100.

Can you get the LCM of 10, 20 and 50 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 20 is 20, and the LCM of 20 and 50 is 100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 100 divisible by 10, 20 and 50?

Yes, and by definition it is the smallest positive integer that is: 100 ÷ 10, 100 ÷ 20 and 100 ÷ 50 all come out whole. Any other common multiple of 10, 20 and 50 is a multiple of 100.

See Also