Least Common Multiple of 96 and 114

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 114 the smallest integer that is 1824 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 114 is 1824.

LCM(96,114) = 1824

LCM of 96 and 114

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

LCM of:
and

Least Common Multiple of 96 and 114

LCM of 96 and 114 is 1824

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 114. First we will calculate the prime factors of 96 and 114.

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 114


2 114
3 57
19 19
1

Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:

114 = 21×31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 114.

LCM(96,114) = 25×31×191
LCM(96,114) = 1824

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 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114

Least Common Multiple of 96 and 114 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 114, than apply into the LCM equation.

GCF(96,114) = 6
LCM(96,114) = ( 96 × 114) / 6
LCM(96,114) = 10944 / 6
LCM(96,114) = 1824

Properties of LCM 96 and 114

(i) The LCM of 114 and 96 is associative

LCM of 96 and 114 = LCM of 114 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 114

Frequently Asked Questions on LCM of 96 and 114

1. What is the LCM of 96 and 114?

Answer: LCM of 96 and 114 is 1824.

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 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

4. How to Find the LCM of 96 and 114?

Answer:

Least Common Multiple of 96 and 114 = 1824

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 114

114 = 2 x 3 x 19

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

LCM = 1824 = 2 x 2 x 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 96 and 114 is 1824.