LCM for 3, 27 and 35

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

What's the Least Common Multiple (LCM) of 3, 27 and 35?

Answer

LCM of 3, 27 and 35 is
945

(Nine hundred forty-five)

945 is the smallest positive integer that 3, 27 and 35 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 27 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 3: 3 (exponent form: 3)

All Prime Factors of 27: 3 × 3 × 3 (exponent form: 33)

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

Prime factor32735Highest power
3333—33
5——55
7——77

LCM = 33 × 5 × 7 = 945

Checking the LCM of 3, 27 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(3, 27) = (3 × 27) ÷ 3 = 81 ÷ 3 = 27

LCM(27, 35) = (27 × 35) ÷ 1 = 945 ÷ 1 = 945

LCM(3, 27, 35) = 945

The pairs may be taken in any order — 27 and 35 first, then 3 — and the answer is the same 945. 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 3, 27 and 35? (The answer is: 945). Enter the first number (e.g. '3'), the second (e.g. '27') 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
32027540
32127189
32227594
32327621
32427216
32527675
32627702
3272727
32728756
32729783
32730270
32731837
32732864
32733297
32734918
32735945
32736108
32737999
327381,026
32739351
327401,080
327411,107
32742378
327431,161
327441,188
32745135
327461,242
327471,269
32748432
327491,323

FAQ

What's the Least Common Multiple (LCM) of 3, 27 and 35?

LCM of 3, 27 and 35 is 945

How to find the LCM of 3, 27 and 35 by prime factorization?

Take every prime that appears in 3, 27 and 35 to the highest power it reaches in any one of them and multiply: 3³ × 5 × 7 = 945.

Can you get the LCM of 3, 27 and 35 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 27 is 27, and the LCM of 27 and 35 is 945 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 945 divisible by 3, 27 and 35?

Yes, and by definition it is the smallest positive integer that is: 945 ÷ 3, 945 ÷ 27 and 945 ÷ 35 all come out whole. Any other common multiple of 3, 27 and 35 is a multiple of 945.

See Also