LCM for 12, 15 and 28

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

What's the Least Common Multiple (LCM) of 12, 15 and 28?

Answer

LCM of 12, 15 and 28 is
420

(Four hundred twenty)

420 is the smallest positive integer that 12, 15 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 15 and 28 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

Prime factor121528Highest power
222—2222
333—3
5—5—5
7——77

LCM = 22 × 3 × 5 × 7 = 420

Checking the LCM of 12, 15 and 28 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, 15) = (12 × 15) ÷ 3 = 180 ÷ 3 = 60

LCM(60, 28) = (60 × 28) ÷ 4 = 1,680 ÷ 4 = 420

LCM(12, 15, 28) = 420

The pairs may be taken in any order — 15 and 28 first, then 12 — and the answer is the same 420. That is exactly why the two routes on this page agree.

Related Calculations

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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, 15 and 28? (The answer is: 420). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '28'), 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
121315780
121415420
12151560
121516240
1215171,020
121518180
1215191,140
12152060
121521420
121522660
1215231,380
121524120
121525300
121526780
121527540
121528420
1215291,740
12153060
1215311,860
121532480
121533660
1215341,020
121535420
121536180
1215372,220
1215381,140
121539780
121540120
1215412,460
121542420

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 28?

LCM of 12, 15 and 28 is 420

How to find the LCM of 12, 15 and 28 by prime factorization?

Take every prime that appears in 12, 15 and 28 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 12, 15 and 28 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 15 is 60, and the LCM of 60 and 28 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 12, 15 and 28?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 15 and 420 ÷ 28 all come out whole. Any other common multiple of 12, 15 and 28 is a multiple of 420.

See Also