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Least Common Multiple of 24 and 32

Free LCM Calculator determines the least common multiple (LCM) between 24 and 32 the smallest integer that is 96 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 32 is 96.

LCM(24,32) = 96

LCM of 24 and 32

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple (LCM) of 24 and 32 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 32. First we will calculate the prime factors of 24 and 32.

Prime Factorization of 24


2 24
2 12
2 6
3 3
1

Prime factors of 24 are 2,3. Prime factorization of 24 in exponential form is:

24 = 23×31

Prime Factorization of 32


2 32
2 16
2 8
2 4
2 2
1

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 32.

LCM(24,32) = 25×31
LCM(24,32) = 96

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1, 2, 4, 8, 16, 32

Least Common Multiple of 24 and 32 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24 and 32, than apply into the LCM equation.

GCF(24,32) = 8
LCM(24,32) = ( 24 × 32) / 8
LCM(24,32) = 768 / 8
LCM(24,32) = 96

Least Common Multiple of 24 and 32 by Listing Multiples

Multiples of 24

24, 48, 72,96

Multiples of 32

32, 64,96

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 24 and 32 is 96

Properties of LCM 24 and 32

(i) The LCM of 32 and 24 is associative

LCM of 24 and 32 = LCM of 32 and 24

Frequently Asked Questions on LCM of 24 and 32

1. What is the LCM of 24 and 32?

Answer: LCM of 24 and 32 is 96.

2. What are the Factors of 24?

Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.

3. What are the Factors of 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

4. How to Find the LCM of 24 and 32?

Answer:

Least Common Multiple of 24 and 32 = 96

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 96 = 2 x 2 x 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 24 and 32 is 96.