LCM for 3, 8 and 11

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

What's the Least Common Multiple (LCM) of 3, 8 and 11?

Answer

LCM of 3, 8 and 11 is
264

(Two hundred sixty-four)

264 is the smallest positive integer that 3, 8 and 11 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 8 and 11 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 11: 11 (exponent form: 11)

Prime factor3811Highest power
2—23—23
33——3
11——1111

LCM = 23 × 3 × 11 = 264

Checking the LCM of 3, 8 and 11 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, 8) = (3 × 8) ÷ 1 = 24 ÷ 1 = 24

LCM(24, 11) = (24 × 11) ÷ 1 = 264 ÷ 1 = 264

LCM(3, 8, 11) = 264

The pairs may be taken in any order — 8 and 11 first, then 3 — and the answer is the same 264. 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, 8 and 11? (The answer is: 264). Enter the first number (e.g. '3'), the second (e.g. '8') and the third (e.g. '11'), 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
13824
23824
33824
34824
358120
36824
378168
38824
38972
3810120
3811264
381224
3813312
3814168
3815120
381648
3817408
381872
3819456
3820120
3821168
3822264
3823552
382424
3825600
3826312
3827216
3828168
3829696
3830120

FAQ

What's the Least Common Multiple (LCM) of 3, 8 and 11?

LCM of 3, 8 and 11 is 264

How to find the LCM of 3, 8 and 11 by prime factorization?

Take every prime that appears in 3, 8 and 11 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 11 = 264.

Can you get the LCM of 3, 8 and 11 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 8 is 24, and the LCM of 24 and 11 is 264 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 264 divisible by 3, 8 and 11?

Yes, and by definition it is the smallest positive integer that is: 264 ÷ 3, 264 ÷ 8 and 264 ÷ 11 all come out whole. Any other common multiple of 3, 8 and 11 is a multiple of 264.

See Also