LCM for 4, 10 and 50

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

What's the Least Common Multiple (LCM) of 4, 10 and 50?

Answer

LCM of 4, 10 and 50 is
100

(One hundred)

100 is the smallest positive integer that 4, 10 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 10 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 4: 2 × 2 (exponent form: 22)

All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

Prime factor41050Highest power
2222222
5—55252

LCM = 22 × 52 = 100

Checking the LCM of 4, 10 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(4, 10) = (4 × 10) ÷ 2 = 40 ÷ 2 = 20

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

LCM(4, 10, 50) = 100

The pairs may be taken in any order — 10 and 50 first, then 4 — 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 4, 10 and 50? (The answer is: 100). Enter the first number (e.g. '4'), the second (e.g. '10') 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
41035140
41036180
41037740
41038380
41039780
4104040
41041820
41042420
41043860
41044220
41045180
41046460
41047940
41048240
41049980
41050100
410511,020
41052260
410531,060
41054540
41055220
41056280
410571,140
41058580
410591,180
4106060
410611,220
41062620
410631,260
41064320

FAQ

What's the Least Common Multiple (LCM) of 4, 10 and 50?

LCM of 4, 10 and 50 is 100

How to find the LCM of 4, 10 and 50 by prime factorization?

Take every prime that appears in 4, 10 and 50 to the highest power it reaches in any one of them and multiply: 2² × 5² = 100.

Can you get the LCM of 4, 10 and 50 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 10 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 4, 10 and 50?

Yes, and by definition it is the smallest positive integer that is: 100 ÷ 4, 100 ÷ 10 and 100 ÷ 50 all come out whole. Any other common multiple of 4, 10 and 50 is a multiple of 100.

See Also