LCM for 20, 28 and 36

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

What's the Least Common Multiple (LCM) of 20, 28 and 36?

Answer

LCM of 20, 28 and 36 is
1,260

(One thousand two hundred sixty)

1,260 is the smallest positive integer that 20, 28 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

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 factor202836Highest power
222222222
3——3232
55——5
7—7—7

LCM = 22 × 32 × 5 × 7 = 1,260

Checking the LCM of 20, 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(20, 28) = (20 × 28) ÷ 4 = 560 ÷ 4 = 140

LCM(140, 36) = (140 × 36) ÷ 4 = 5,040 ÷ 4 = 1,260

LCM(20, 28, 36) = 1,260

The pairs may be taken in any order — 28 and 36 first, then 20 — and the answer is the same 1,260. 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 20, 28 and 36? (The answer is: 1,260). Enter the first number (e.g. '20'), 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
202128420
2022281,540
2023283,220
202428840
202528700
2026281,820
2027283,780
202828140
2028294,060
202830420
2028314,340
2028321,120
2028334,620
2028342,380
202835140
2028361,260
2028375,180
2028382,660
2028395,460
202840280
2028415,740
202842420
2028436,020
2028441,540
2028451,260
2028463,220
2028476,580
2028481,680
202849980
202850700

FAQ

What's the Least Common Multiple (LCM) of 20, 28 and 36?

LCM of 20, 28 and 36 is 1,260

How to find the LCM of 20, 28 and 36 by prime factorization?

Take every prime that appears in 20, 28 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 × 7 = 1,260.

Can you get the LCM of 20, 28 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 20 and 28 is 140, and the LCM of 140 and 36 is 1,260 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,260 divisible by 20, 28 and 36?

Yes, and by definition it is the smallest positive integer that is: 1,260 ÷ 20, 1,260 ÷ 28 and 1,260 ÷ 36 all come out whole. Any other common multiple of 20, 28 and 36 is a multiple of 1,260.

See Also