Least Common Multiple of 9 and 24

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 9 and 24 the smallest integer that is 72 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 24 is 72.

LCM(9,24) = 72

LCM of 9 and 24

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

LCM of:
and

Least Common Multiple of 9 and 24

LCM of 9 and 24 is 72

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 24. First we will calculate the prime factors of 9 and 24.

Prime Factorization of 9


3 9
3 3
1

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 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

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 24.

LCM(9,24) = 23×32
LCM(9,24) = 72

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

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 9 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 9 and 24, than apply into the LCM equation.

GCF(9,24) = 3
LCM(9,24) = ( 9 × 24) / 3
LCM(9,24) = 216 / 3
LCM(9,24) = 72

Properties of LCM 9 and 24

(i) The LCM of 24 and 9 is associative

LCM of 9 and 24 = LCM of 24 and 9

Frequently Asked Questions on LCM of 9 and 24

1. What is the LCM of 9 and 24?

Answer: LCM of 9 and 24 is 72.

2. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

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 9 and 24?

Answer:

Least Common Multiple of 9 and 24 = 72

Step 1: Find the prime factorization of 9

9 = 3 x 3

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 = 72 = 2 x 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 9 and 24 is 72.