LCM for 4, 16 and 36

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

What's the Least Common Multiple (LCM) of 4, 16 and 36?

Answer

LCM of 4, 16 and 36 is
144

(One hundred forty-four)

144 is the smallest positive integer that 4, 16 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 16 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

Prime factor41636Highest power
222242224
3——3232

LCM = 24 × 32 = 144

Checking the LCM of 4, 16 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, 16) = (4 × 16) ÷ 4 = 64 ÷ 4 = 16

LCM(16, 36) = (16 × 36) ÷ 4 = 576 ÷ 4 = 144

LCM(4, 16, 36) = 144

The pairs may be taken in any order — 16 and 36 first, then 4 — and the answer is the same 144. That is exactly why the two routes on this page agree.

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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 4, 16 and 36? (The answer is: 144). Enter the first number (e.g. '4'), the second (e.g. '16') 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
41621336
41622176
41623368
4162448
41625400
41626208
41627432
41628112
41629464
41630240
41631496
4163232
41633528
41634272
41635560
41636144
41637592
41638304
41639624
4164080
41641656
41642336
41643688
41644176
41645720
41646368
41647752
4164848
41649784
41650400

FAQ

What's the Least Common Multiple (LCM) of 4, 16 and 36?

LCM of 4, 16 and 36 is 144

How to find the LCM of 4, 16 and 36 by prime factorization?

Take every prime that appears in 4, 16 and 36 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 4, 16 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 16 is 16, and the LCM of 16 and 36 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 4, 16 and 36?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 4, 144 ÷ 16 and 144 ÷ 36 all come out whole. Any other common multiple of 4, 16 and 36 is a multiple of 144.

See Also