Least Common Multiple of 96 and 97

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 97 the smallest integer that is 9312 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 97 is 9312.

LCM(96,97) = 9312

LCM of 96 and 97

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

LCM of:
and

Least Common Multiple of 96 and 97

LCM of 96 and 97 is 9312

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 97. First we will calculate the prime factors of 96 and 97.

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 97


97 97
1

Prime factors of 97 are 97. Prime factorization of 97 in exponential form is:

97 = 971

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 97.

LCM(96,97) = 25×31×971
LCM(96,97) = 9312

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 97

List of positive integer factors of 97 that divides 97 without a remainder.

1, 97

Least Common Multiple of 96 and 97 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 97, than apply into the LCM equation.

GCF(96,97) = 1
LCM(96,97) = ( 96 × 97) / 1
LCM(96,97) = 9312 / 1
LCM(96,97) = 9312

Properties of LCM 96 and 97

(i) The LCM of 97 and 96 is associative

LCM of 96 and 97 = LCM of 97 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 97

Frequently Asked Questions on LCM of 96 and 97

1. What is the LCM of 96 and 97?

Answer: LCM of 96 and 97 is 9312.

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 97?

Answer: Factors of 97 are 1, 97. There are 2 integers that are factors of 97. The greatest factor of 97 is 97.

4. How to Find the LCM of 96 and 97?

Answer:

Least Common Multiple of 96 and 97 = 9312

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 97

97 = 97

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

LCM = 9312 = 2 x 2 x 2 x 2 x 2 x 3 x 97

Step 4: Therefore, the least common multiple of 96 and 97 is 9312.