Least Common Multiple of 89 and 96

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 89 and 96 the smallest integer that is 8544 that is divisible by both numbers.

Least Common Multiple (LCM) of 89 and 96 is 8544.

LCM(89,96) = 8544

LCM of 89 and 96

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

LCM of:
and

Least Common Multiple of 89 and 96

LCM of 89 and 96 is 8544

Least common multiple can be found by multiplying the highest exponent prime factors of 89 and 96. First we will calculate the prime factors of 89 and 96.

Prime Factorization of 89


89 89
1

Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:

89 = 891

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

Now multiplying the highest exponent prime factors to calculate the LCM of 89 and 96.

LCM(89,96) = 25×31×891
LCM(89,96) = 8544

Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

1, 89

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

Least Common Multiple of 89 and 96 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89 and 96, than apply into the LCM equation.

GCF(89,96) = 1
LCM(89,96) = ( 89 × 96) / 1
LCM(89,96) = 8544 / 1
LCM(89,96) = 8544

Properties of LCM 89 and 96

(i) The LCM of 96 and 89 is associative

LCM of 89 and 96 = LCM of 96 and 89

Related Least Common Multiples of 89

Related Least Common Multiples of 96

Frequently Asked Questions on LCM of 89 and 96

1. What is the LCM of 89 and 96?

Answer: LCM of 89 and 96 is 8544.

2. What are the Factors of 89?

Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.

3. 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.

4. How to Find the LCM of 89 and 96?

Answer:

Least Common Multiple of 89 and 96 = 8544

Step 1: Find the prime factorization of 89

89 = 89

Step 2: Find the prime factorization of 96

96 = 2 x 2 x 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 = 8544 = 2 x 2 x 2 x 2 x 2 x 3 x 89

Step 4: Therefore, the least common multiple of 89 and 96 is 8544.