LCM for 16, 36 and 48

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 16, 36 and 48?

Answer

LCM of 16, 36 and 48 is
144

(One hundred forty-four)

144 is the smallest positive integer that 16, 36 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 16, 36 and 48 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

Prime factor163648Highest power
224222424
3—32332

LCM = 24 × 32 = 144

Checking the LCM of 16, 36 and 48 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(16, 36) = (16 × 36) ÷ 4 = 576 ÷ 4 = 144

LCM(144, 48) = (144 × 48) ÷ 48 = 6,912 ÷ 48 = 144

LCM(16, 36, 48) = 144

The pairs may be taken in any order — 36 and 48 first, then 16 — 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 16, 36 and 48? (The answer is: 144). Enter the first number (e.g. '16'), the second (e.g. '36') and the third (e.g. '48'), 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
1633361,584
1634362,448
1635365,040
163636144
1636375,328
1636382,736
1636391,872
163640720
1636415,904
1636421,008
1636436,192
1636441,584
163645720
1636463,312
1636476,768
163648144
1636497,056
1636503,600
1636512,448
1636521,872
1636537,632
163654432
1636557,920
1636561,008
1636572,736
1636584,176
1636598,496
163660720
1636618,784
1636624,464

FAQ

What's the Least Common Multiple (LCM) of 16, 36 and 48?

LCM of 16, 36 and 48 is 144

How to find the LCM of 16, 36 and 48 by prime factorization?

Take every prime that appears in 16, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 16, 36 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 36 is 144, and the LCM of 144 and 48 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 16, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 16, 144 ÷ 36 and 144 ÷ 48 all come out whole. Any other common multiple of 16, 36 and 48 is a multiple of 144.

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