LCM for 24, 32 and 48

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

What's the Least Common Multiple (LCM) of 24, 32 and 48?

Answer

LCM of 24, 32 and 48 is
96

(Ninety-six)

96 is the smallest positive integer that 24, 32 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 24, 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

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 factor243248Highest power
223252425
33—33

LCM = 25 × 3 = 96

Checking the LCM of 24, 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(24, 32) = (24 × 32) ÷ 8 = 768 ÷ 8 = 96

LCM(96, 48) = (96 × 48) ÷ 48 = 4,608 ÷ 48 = 96

LCM(24, 32, 48) = 96

The pairs may be taken in any order — 32 and 48 first, then 24 — and the answer is the same 96. 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 24, 32 and 48? (The answer is: 96). Enter the first number (e.g. '24'), 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
2432331,056
2432341,632
2432353,360
243236288
2432373,552
2432381,824
2432391,248
243240480
2432413,936
243242672
2432434,128
2432441,056
2432451,440
2432462,208
2432474,512
24324896
2432494,704
2432502,400
2432511,632
2432521,248
2432535,088
243254864
2432555,280
243256672
2432571,824
2432582,784
2432595,664
243260480
2432615,856
2432622,976

FAQ

What's the Least Common Multiple (LCM) of 24, 32 and 48?

LCM of 24, 32 and 48 is 96

How to find the LCM of 24, 32 and 48 by prime factorization?

Take every prime that appears in 24, 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 24, 32 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 24 and 32 is 96, and the LCM of 96 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 24, 32 and 48?

Yes, and by definition it is the smallest positive integer that is: 96 ÷ 24, 96 ÷ 32 and 96 ÷ 48 all come out whole. Any other common multiple of 24, 32 and 48 is a multiple of 96.

See Also