LCM for 16, 32 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, 32 and 48?

Answer

LCM of 16, 32 and 48 is
96

(Ninety-six)

96 is the smallest positive integer that 16, 32 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 16, 32 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 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

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

Prime factor163248Highest power
224252425
3——33

LCM = 25 × 3 = 96

Checking the LCM of 16, 32 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, 32) = (16 × 32) ÷ 16 = 512 ÷ 16 = 32

LCM(32, 48) = (32 × 48) ÷ 16 = 1,536 ÷ 16 = 96

LCM(16, 32, 48) = 96

The pairs may be taken in any order — 32 and 48 first, then 16 — and the answer is the same 96. 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 16, 32 and 48? (The answer is: 96). Enter the first number (e.g. '16'), the second (e.g. '32') 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
1632331,056
163234544
1632351,120
163236288
1632371,184
163238608
1632391,248
163240160
1632411,312
163242672
1632431,376
163244352
1632451,440
163246736
1632471,504
16324896
1632491,568
163250800
1632511,632
163252416
1632531,696
163254864
1632551,760
163256224
1632571,824
163258928
1632591,888
163260480
1632611,952
163262992

FAQ

What's the Least Common Multiple (LCM) of 16, 32 and 48?

LCM of 16, 32 and 48 is 96

How to find the LCM of 16, 32 and 48 by prime factorization?

Take every prime that appears in 16, 32 and 48 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 = 96.

Can you get the LCM of 16, 32 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 32 is 32, and the LCM of 32 and 48 is 96 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 96 divisible by 16, 32 and 48?

Yes, and by definition it is the smallest positive integer that is: 96 ÷ 16, 96 ÷ 32 and 96 ÷ 48 all come out whole. Any other common multiple of 16, 32 and 48 is a multiple of 96.

See Also