LCM for 35, 60 and 100

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

What's the Least Common Multiple (LCM) of 35, 60 and 100?

Answer

LCM of 35, 60 and 100 is
2,100

(Two thousand one hundred)

2,100 is the smallest positive integer that 35, 60 and 100 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 35, 60 and 100 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 35: 5 × 7 (exponent form: 5 × 7)

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

Prime factor3560100Highest power
2—222222
3—3—3
5555252
77——7

LCM = 22 × 3 × 52 × 7 = 2,100

Checking the LCM of 35, 60 and 100 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(35, 60) = (35 × 60) ÷ 5 = 2,100 ÷ 5 = 420

LCM(420, 100) = (420 × 100) ÷ 20 = 42,000 ÷ 20 = 2,100

LCM(35, 60, 100) = 2,100

The pairs may be taken in any order — 60 and 100 first, then 35 — and the answer is the same 2,100. 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 35, 60 and 100? (The answer is: 2,100). Enter the first number (e.g. '35'), the second (e.g. '60') and the third (e.g. '100'), 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
3560857,140
35608618,060
35608712,180
3560889,240
35608937,380
3560901,260
3560915,460
3560929,660
35609313,020
35609419,740
3560957,980
3560963,360
35609740,740
3560982,940
35609913,860
35601002,100
356010142,420
35601027,140
356010343,260
356010410,920
3560105420
356010622,260
356010744,940
35601083,780
356010945,780
35601104,620
356011115,540
35601121,680
356011347,460
35601147,980

FAQ

What's the Least Common Multiple (LCM) of 35, 60 and 100?

LCM of 35, 60 and 100 is 2,100

How to find the LCM of 35, 60 and 100 by prime factorization?

Take every prime that appears in 35, 60 and 100 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² × 7 = 2,100.

Can you get the LCM of 35, 60 and 100 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 35 and 60 is 420, and the LCM of 420 and 100 is 2,100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 2,100 divisible by 35, 60 and 100?

Yes, and by definition it is the smallest positive integer that is: 2,100 ÷ 35, 2,100 ÷ 60 and 2,100 ÷ 100 all come out whole. Any other common multiple of 35, 60 and 100 is a multiple of 2,100.

See Also