LCM for 10, 20 and 40

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

What's the Least Common Multiple (LCM) of 10, 20 and 40?

Answer

LCM of 10, 20 and 40 is
40

(Forty)

40 is the smallest positive integer that 10, 20 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

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)

Prime factor102040Highest power
22222323
55555

LCM = 23 × 5 = 40

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

LCM(20, 40) = (20 × 40) ÷ 20 = 800 ÷ 20 = 40

LCM(10, 20, 40) = 40

The pairs may be taken in any order — 20 and 40 first, then 10 — and the answer is the same 40. 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 40? (The answer is: 40). Enter the first number (e.g. '10'), the second (e.g. '20') 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
102025100
102026260
102027540
102028140
102029580
10203060
102031620
102032160
102033660
102034340
102035140
102036180
102037740
102038380
102039780
10204040
102041820
102042420
102043860
102044220
102045180
102046460
102047940
102048240
102049980
102050100
1020511,020
102052260
1020531,060
102054540

FAQ

What's the Least Common Multiple (LCM) of 10, 20 and 40?

LCM of 10, 20 and 40 is 40

How to find the LCM of 10, 20 and 40 by prime factorization?

Take every prime that appears in 10, 20 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 5 = 40.

Can you get the LCM of 10, 20 and 40 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 40 is 40 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 40 divisible by 10, 20 and 40?

Yes, and by definition it is the smallest positive integer that is: 40 ÷ 10, 40 ÷ 20 and 40 ÷ 40 all come out whole. Any other common multiple of 10, 20 and 40 is a multiple of 40.

See Also