LCM for 12, 30 and 40

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

What's the Least Common Multiple (LCM) of 12, 30 and 40?

Answer

LCM of 12, 30 and 40 is
120

(One hundred twenty)

120 is the smallest positive integer that 12, 30 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 30 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

Prime factor123040Highest power
22222323
333—3
5—555

LCM = 23 × 3 × 5 = 120

Checking the LCM of 12, 30 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(12, 30) = (12 × 30) ÷ 6 = 360 ÷ 6 = 60

LCM(60, 40) = (60 × 40) ÷ 20 = 2,400 ÷ 20 = 120

LCM(12, 30, 40) = 120

The pairs may be taken in any order — 30 and 40 first, then 12 — and the answer is the same 120. That is exactly why the two routes on this page agree.

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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 12, 30 and 40? (The answer is: 120). Enter the first number (e.g. '12'), the second (e.g. '30') 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
122530300
122630780
122730540
122830420
1229301,740
12303060
1230311,860
123032480
123033660
1230341,020
123035420
123036180
1230372,220
1230381,140
123039780
123040120
1230412,460
123042420
1230432,580
123044660
123045180
1230461,380
1230472,820
123048240
1230492,940
123050300
1230511,020
123052780
1230533,180
123054540

FAQ

What's the Least Common Multiple (LCM) of 12, 30 and 40?

LCM of 12, 30 and 40 is 120

How to find the LCM of 12, 30 and 40 by prime factorization?

Take every prime that appears in 12, 30 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 12, 30 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 30 is 60, and the LCM of 60 and 40 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 12, 30 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 12, 120 ÷ 30 and 120 ÷ 40 all come out whole. Any other common multiple of 12, 30 and 40 is a multiple of 120.

See Also