LCM for 3, 12 and 30

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

What's the Least Common Multiple (LCM) of 3, 12 and 30?

Answer

LCM of 3, 12 and 30 is
60

(Sixty)

60 is the smallest positive integer that 3, 12 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 12 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 3: 3 (exponent form: 3)

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)

Prime factor31230Highest power
2—22222
33333
5——55

LCM = 22 × 3 × 5 = 60

Checking the LCM of 3, 12 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(3, 12) = (3 × 12) ÷ 3 = 36 ÷ 3 = 12

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

LCM(3, 12, 30) = 60

The pairs may be taken in any order — 12 and 30 first, then 3 — and the answer is the same 60. 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 3, 12 and 30? (The answer is: 60). Enter the first number (e.g. '3'), the second (e.g. '12') 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
3121560
3121648
31217204
3121836
31219228
3122060
3122184
31222132
31223276
3122424
31225300
31226156
31227108
3122884
31229348
3123060
31231372
3123296
31233132
31234204
31235420
3123636
31237444
31238228
31239156
31240120
31241492
3124284
31243516
31244132

FAQ

What's the Least Common Multiple (LCM) of 3, 12 and 30?

LCM of 3, 12 and 30 is 60

How to find the LCM of 3, 12 and 30 by prime factorization?

Take every prime that appears in 3, 12 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 3, 12 and 30 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 12 is 12, and the LCM of 12 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 3, 12 and 30?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 3, 60 ÷ 12 and 60 ÷ 30 all come out whole. Any other common multiple of 3, 12 and 30 is a multiple of 60.

See Also