LCM for 7, 20 and 35

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

What's the Least Common Multiple (LCM) of 7, 20 and 35?

Answer

LCM of 7, 20 and 35 is
140

(One hundred forty)

140 is the smallest positive integer that 7, 20 and 35 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

All Prime Factors of 35: 5 × 7 (exponent form: 5 × 7)

Prime factor72035Highest power
2—22—22
5—555
77—77

LCM = 22 × 5 × 7 = 140

Checking the LCM of 7, 20 and 35 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(7, 20) = (7 × 20) ÷ 1 = 140 ÷ 1 = 140

LCM(140, 35) = (140 × 35) ÷ 35 = 4,900 ÷ 35 = 140

LCM(7, 20, 35) = 140

The pairs may be taken in any order — 20 and 35 first, then 7 — and the answer is the same 140. 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 7, 20 and 35? (The answer is: 140). Enter the first number (e.g. '7'), the second (e.g. '20') and the third (e.g. '35'), 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
72020140
72021420
720221,540
720233,220
72024840
72025700
720261,820
720273,780
72028140
720294,060
72030420
720314,340
720321,120
720334,620
720342,380
72035140
720361,260
720375,180
720382,660
720395,460
72040280
720415,740
72042420
720436,020
720441,540
720451,260
720463,220
720476,580
720481,680
72049980

FAQ

What's the Least Common Multiple (LCM) of 7, 20 and 35?

LCM of 7, 20 and 35 is 140

How to find the LCM of 7, 20 and 35 by prime factorization?

Take every prime that appears in 7, 20 and 35 to the highest power it reaches in any one of them and multiply: 2² × 5 × 7 = 140.

Can you get the LCM of 7, 20 and 35 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 7 and 20 is 140, and the LCM of 140 and 35 is 140 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 140 divisible by 7, 20 and 35?

Yes, and by definition it is the smallest positive integer that is: 140 ÷ 7, 140 ÷ 20 and 140 ÷ 35 all come out whole. Any other common multiple of 7, 20 and 35 is a multiple of 140.

See Also