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Least Common Multiple of 16 and 24

Free LCM Calculator determines the least common multiple (LCM) between 16 and 24 the smallest integer that is 48 that is divisible by both numbers.

Least Common Multiple (LCM) of 16 and 24 is 48.

LCM(16,24) = 48

LCM of 16 and 24

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

LCM of:
and

Least Common Multiple (LCM) of 16 and 24 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16 and 24. First we will calculate the prime factors of 16 and 24.

Prime Factorization of 16


2 16
2 8
2 4
2 2
1

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

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

Now multiplying the highest exponent prime factors to calculate the LCM of 16 and 24.

LCM(16,24) = 24×31
LCM(16,24) = 48

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1, 2, 4, 8, 16

Factors of 24

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

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

Least Common Multiple of 16 and 24 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16 and 24, than apply into the LCM equation.

GCF(16,24) = 8
LCM(16,24) = ( 16 × 24) / 8
LCM(16,24) = 384 / 8
LCM(16,24) = 48

Least Common Multiple of 16 and 24 by Listing Multiples

Multiples of 16

16, 32,48

Multiples of 24

24,48

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

∴ Least Common Multiple of 16 and 24 is 48

Properties of LCM 16 and 24

(i) The LCM of 24 and 16 is associative

LCM of 16 and 24 = LCM of 24 and 16

Frequently Asked Questions on LCM of 16 and 24

1. What is the LCM of 16 and 24?

Answer: LCM of 16 and 24 is 48.

2. What are the Factors of 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

3. 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.

4. How to Find the LCM of 16 and 24?

Answer:

Least Common Multiple of 16 and 24 = 48

Step 1: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

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

LCM = 48 = 2 x 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 16 and 24 is 48.