Least Common Multiple of 96 and 107

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 107 the smallest integer that is 10272 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 107 is 10272.

LCM(96,107) = 10272

LCM of 96 and 107

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

LCM of:
and

Least Common Multiple of 96 and 107

LCM of 96 and 107 is 10272

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 107. First we will calculate the prime factors of 96 and 107.

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 107


107 107
1

Prime factors of 107 are 107. Prime factorization of 107 in exponential form is:

107 = 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 107.

LCM(96,107) = 25×31×1071
LCM(96,107) = 10272

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 107

List of positive integer factors of 107 that divides 107 without a remainder.

1, 107

Least Common Multiple of 96 and 107 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 107, than apply into the LCM equation.

GCF(96,107) = 1
LCM(96,107) = ( 96 × 107) / 1
LCM(96,107) = 10272 / 1
LCM(96,107) = 10272

Properties of LCM 96 and 107

(i) The LCM of 107 and 96 is associative

LCM of 96 and 107 = LCM of 107 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 107

Frequently Asked Questions on LCM of 96 and 107

1. What is the LCM of 96 and 107?

Answer: LCM of 96 and 107 is 10272.

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 107?

Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.

4. How to Find the LCM of 96 and 107?

Answer:

Least Common Multiple of 96 and 107 = 10272

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 107

107 = 107

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

LCM = 10272 = 2 x 2 x 2 x 2 x 2 x 3 x 107

Step 4: Therefore, the least common multiple of 96 and 107 is 10272.