LCM for 4, 27 and 36

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

What's the Least Common Multiple (LCM) of 4, 27 and 36?

Answer

LCM of 4, 27 and 36 is
108

(One hundred eight)

108 is the smallest positive integer that 4, 27 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 27 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 4: 2 × 2 (exponent form: 22)

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

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor42736Highest power
222—2222
3—333233

LCM = 22 × 33 = 108

Checking the LCM of 4, 27 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(4, 27) = (4 × 27) ÷ 1 = 108 ÷ 1 = 108

LCM(108, 36) = (108 × 36) ÷ 36 = 3,888 ÷ 36 = 108

LCM(4, 27, 36) = 108

The pairs may be taken in any order — 27 and 36 first, then 4 — and the answer is the same 108. 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 4, 27 and 36? (The answer is: 108). Enter the first number (e.g. '4'), the second (e.g. '27') 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
42127756
422271,188
423272,484
42427216
425272,700
426271,404
42727108
42728756
427293,132
42730540
427313,348
42732864
427331,188
427341,836
427353,780
42736108
427373,996
427382,052
427391,404
427401,080
427414,428
42742756
427434,644
427441,188
42745540
427462,484
427475,076
42748432
427495,292
427502,700

FAQ

What's the Least Common Multiple (LCM) of 4, 27 and 36?

LCM of 4, 27 and 36 is 108

How to find the LCM of 4, 27 and 36 by prime factorization?

Take every prime that appears in 4, 27 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3³ = 108.

Can you get the LCM of 4, 27 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 27 is 108, and the LCM of 108 and 36 is 108 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 108 divisible by 4, 27 and 36?

Yes, and by definition it is the smallest positive integer that is: 108 ÷ 4, 108 ÷ 27 and 108 ÷ 36 all come out whole. Any other common multiple of 4, 27 and 36 is a multiple of 108.

See Also