Least Common Multiple of 96 and 109

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 96 and 109 the smallest integer that is 10464 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 109 is 10464.

LCM(96,109) = 10464

LCM of 96 and 109

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

LCM of:
and

Least Common Multiple of 96 and 109

LCM of 96 and 109 is 10464

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 109. First we will calculate the prime factors of 96 and 109.

Prime Factorization of 96


2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:

96 = 25×31

Prime Factorization of 109


109 109
1

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 109.

LCM(96,109) = 25×31×1091
LCM(96,109) = 10464

Factors of 96

List of positive integer factors of 96 that divides 96 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 109

List of positive integer factors of 109 that divides 109 without a remainder.

1, 109

Least Common Multiple of 96 and 109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96 and 109, than apply into the LCM equation.

GCF(96,109) = 1
LCM(96,109) = ( 96 × 109) / 1
LCM(96,109) = 10464 / 1
LCM(96,109) = 10464

Properties of LCM 96 and 109

(i) The LCM of 109 and 96 is associative

LCM of 96 and 109 = LCM of 109 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 109

Frequently Asked Questions on LCM of 96 and 109

1. What is the LCM of 96 and 109?

Answer: LCM of 96 and 109 is 10464.

2. What are the Factors of 96?

Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.

3. What are the Factors of 109?

Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.

4. How to Find the LCM of 96 and 109?

Answer:

Least Common Multiple of 96 and 109 = 10464

Step 1: Find the prime factorization of 96

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

Step 2: Find the prime factorization of 109

109 = 109

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

LCM = 10464 = 2 x 2 x 2 x 2 x 2 x 3 x 109

Step 4: Therefore, the least common multiple of 96 and 109 is 10464.