LCM for 4, 12 and 15

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

What's the Least Common Multiple (LCM) of 4, 12 and 15?

Answer

LCM of 4, 12 and 15 is
60

(Sixty)

60 is the smallest positive integer that 4, 12 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 12 and 15 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

Prime factor41215Highest power
22222—22
3—333
5——55

LCM = 22 × 3 × 5 = 60

Checking the LCM of 4, 12 and 15 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, 12) = (4 × 12) ÷ 4 = 48 ÷ 4 = 12

LCM(12, 15) = (12 × 15) ÷ 3 = 180 ÷ 3 = 60

LCM(4, 12, 15) = 60

The pairs may be taken in any order — 12 and 15 first, then 4 — 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 4, 12 and 15? (The answer is: 60). Enter the first number (e.g. '4'), the second (e.g. '12') and the third (e.g. '15'), 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
141212
241212
341212
441212
451260
461212
471284
481224
491236
4101260
41112132
4121212
41213156
4121484
4121560
4121648
41217204
4121836
41219228
4122060
4122184
41222132
41223276
4122424
41225300
41226156
41227108
4122884
41229348
4123060

FAQ

What's the Least Common Multiple (LCM) of 4, 12 and 15?

LCM of 4, 12 and 15 is 60

How to find the LCM of 4, 12 and 15 by prime factorization?

Take every prime that appears in 4, 12 and 15 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 4, 12 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 12 is 12, and the LCM of 12 and 15 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 4, 12 and 15?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 4, 60 ÷ 12 and 60 ÷ 15 all come out whole. Any other common multiple of 4, 12 and 15 is a multiple of 60.

See Also