LCM for 20, 35 and 45

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

What's the Least Common Multiple (LCM) of 20, 35 and 45?

Answer

LCM of 20, 35 and 45 is
1,260

(One thousand two hundred sixty)

1,260 is the smallest positive integer that 20, 35 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 35 and 45 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 35: 5 × 7 (exponent form: 5 × 7)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor203545Highest power
222——22
3——3232
55555
7—7—7

LCM = 22 × 32 × 5 × 7 = 1,260

Checking the LCM of 20, 35 and 45 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, 35) = (20 × 35) ÷ 5 = 700 ÷ 5 = 140

LCM(140, 45) = (140 × 45) ÷ 5 = 6,300 ÷ 5 = 1,260

LCM(20, 35, 45) = 1,260

The pairs may be taken in any order — 35 and 45 first, then 20 — and the answer is the same 1,260. 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 20, 35 and 45? (The answer is: 1,260). Enter the first number (e.g. '20'), the second (e.g. '35') and the third (e.g. '45'), 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
203035420
2031354,340
2032351,120
2033354,620
2034352,380
203535140
2035361,260
2035375,180
2035382,660
2035395,460
203540280
2035415,740
203542420
2035436,020
2035441,540
2035451,260
2035463,220
2035476,580
2035481,680
203549980
203550700
2035517,140
2035521,820
2035537,420
2035543,780
2035551,540
203556280
2035577,980
2035584,060
2035598,260

FAQ

What's the Least Common Multiple (LCM) of 20, 35 and 45?

LCM of 20, 35 and 45 is 1,260

How to find the LCM of 20, 35 and 45 by prime factorization?

Take every prime that appears in 20, 35 and 45 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, 35 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 20 and 35 is 140, and the LCM of 140 and 45 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, 35 and 45?

Yes, and by definition it is the smallest positive integer that is: 1,260 ÷ 20, 1,260 ÷ 35 and 1,260 ÷ 45 all come out whole. Any other common multiple of 20, 35 and 45 is a multiple of 1,260.

See Also