LCM for 10, 20 and 30

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

What's the Least Common Multiple (LCM) of 10, 20 and 30?

Answer

LCM of 10, 20 and 30 is
60

(Sixty)

60 is the smallest positive integer that 10, 20 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 20 and 30 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

Prime factor102030Highest power
2222222
3——33
55555

LCM = 22 × 3 × 5 = 60

Checking the LCM of 10, 20 and 30 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, 30) = (20 × 30) ÷ 10 = 600 ÷ 10 = 60

LCM(10, 20, 30) = 60

The pairs may be taken in any order — 20 and 30 first, then 10 — and the answer is the same 60. That is exactly why the two routes on this page agree.

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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 30? (The answer is: 60). Enter the first number (e.g. '10'), the second (e.g. '20') and the third (e.g. '30'), 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
10152060
10162080
101720340
101820180
101920380
10202020
102021420
102022220
102023460
102024120
102025100
102026260
102027540
102028140
102029580
10203060
102031620
102032160
102033660
102034340
102035140
102036180
102037740
102038380
102039780
10204040
102041820
102042420
102043860
102044220

FAQ

What's the Least Common Multiple (LCM) of 10, 20 and 30?

LCM of 10, 20 and 30 is 60

How to find the LCM of 10, 20 and 30 by prime factorization?

Take every prime that appears in 10, 20 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 10, 20 and 30 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 30 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 10, 20 and 30?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 10, 60 ÷ 20 and 60 ÷ 30 all come out whole. Any other common multiple of 10, 20 and 30 is a multiple of 60.

See Also