LCM for 12, 28 and 36

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 12, 28 and 36?

Answer

LCM of 12, 28 and 36 is
252

(Two hundred fifty-two)

252 is the smallest positive integer that 12, 28 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 28 and 36 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor122836Highest power
222222222
33—3232
7—7—7

LCM = 22 × 32 × 7 = 252

Checking the LCM of 12, 28 and 36 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, 28) = (12 × 28) ÷ 4 = 336 ÷ 4 = 84

LCM(84, 36) = (84 × 36) ÷ 12 = 3,024 ÷ 12 = 252

LCM(12, 28, 36) = 252

The pairs may be taken in any order — 28 and 36 first, then 12 — and the answer is the same 252. 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, 28 and 36? (The answer is: 252). Enter the first number (e.g. '12'), the second (e.g. '28') and the third (e.g. '36'), 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
12212884
122228924
1223281,932
122428168
1225282,100
1226281,092
122728756
12282884
1228292,436
122830420
1228312,604
122832672
122833924
1228341,428
122835420
122836252
1228373,108
1228381,596
1228391,092
122840840
1228413,444
12284284
1228433,612
122844924
1228451,260
1228461,932
1228473,948
122848336
122849588
1228502,100

FAQ

What's the Least Common Multiple (LCM) of 12, 28 and 36?

LCM of 12, 28 and 36 is 252

How to find the LCM of 12, 28 and 36 by prime factorization?

Take every prime that appears in 12, 28 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

Can you get the LCM of 12, 28 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 28 is 84, and the LCM of 84 and 36 is 252 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 252 divisible by 12, 28 and 36?

Yes, and by definition it is the smallest positive integer that is: 252 ÷ 12, 252 ÷ 28 and 252 ÷ 36 all come out whole. Any other common multiple of 12, 28 and 36 is a multiple of 252.

See Also