LCM for 3, 4 and 11

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

What's the Least Common Multiple (LCM) of 3, 4 and 11?

Answer

LCM of 3, 4 and 11 is
132

(One hundred thirty-two)

132 is the smallest positive integer that 3, 4 and 11 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 4 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 4: 2 × 2 (exponent form: 22)

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

Prime factor3411Highest power
2—22—22
33——3
11——1111

LCM = 22 × 3 × 11 = 132

Checking the LCM of 3, 4 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, 4) = (3 × 4) ÷ 1 = 12 ÷ 1 = 12

LCM(12, 11) = (12 × 11) ÷ 1 = 132 ÷ 1 = 132

LCM(3, 4, 11) = 132

The pairs may be taken in any order — 4 and 11 first, then 3 — and the answer is the same 132. That is exactly why the two routes on this page agree.

Related Calculations

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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 3, 4 and 11? (The answer is: 132). Enter the first number (e.g. '3'), the second (e.g. '4') 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
13412
23412
33412
34412
34560
34612
34784
34824
34936
341060
3411132
341212
3413156
341484
341560
341648
3417204
341836
3419228
342060
342184
3422132
3423276
342424
3425300
3426156
3427108
342884
3429348
343060

FAQ

What's the Least Common Multiple (LCM) of 3, 4 and 11?

LCM of 3, 4 and 11 is 132

How to find the LCM of 3, 4 and 11 by prime factorization?

Take every prime that appears in 3, 4 and 11 to the highest power it reaches in any one of them and multiply: 2² × 3 × 11 = 132.

Can you get the LCM of 3, 4 and 11 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 4 is 12, and the LCM of 12 and 11 is 132 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 132 divisible by 3, 4 and 11?

Yes, and by definition it is the smallest positive integer that is: 132 ÷ 3, 132 ÷ 4 and 132 ÷ 11 all come out whole. Any other common multiple of 3, 4 and 11 is a multiple of 132.

See Also