LCM for 12, 20 and 28

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

What's the Least Common Multiple (LCM) of 12, 20 and 28?

Answer

LCM of 12, 20 and 28 is
420

(Four hundred twenty)

420 is the smallest positive integer that 12, 20 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 20 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

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

Prime factor122028Highest power
222222222
33——3
5—5—5
7——77

LCM = 22 × 3 × 5 × 7 = 420

Checking the LCM of 12, 20 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, 20) = (12 × 20) ÷ 4 = 240 ÷ 4 = 60

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

LCM(12, 20, 28) = 420

The pairs may be taken in any order — 20 and 28 first, then 12 — and the answer is the same 420. 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, 20 and 28? (The answer is: 420). Enter the first number (e.g. '12'), the second (e.g. '20') 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
121320780
121420420
12152060
121620240
1217201,020
121820180
1219201,140
12202060
122021420
122022660
1220231,380
122024120
122025300
122026780
122027540
122028420
1220291,740
12203060
1220311,860
122032480
122033660
1220341,020
122035420
122036180
1220372,220
1220381,140
122039780
122040120
1220412,460
122042420

FAQ

What's the Least Common Multiple (LCM) of 12, 20 and 28?

LCM of 12, 20 and 28 is 420

How to find the LCM of 12, 20 and 28 by prime factorization?

Take every prime that appears in 12, 20 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, 20 and 28 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 20 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, 20 and 28?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 20 and 420 ÷ 28 all come out whole. Any other common multiple of 12, 20 and 28 is a multiple of 420.

See Also