Least Common Multiple of 96 and 103

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 103 the smallest integer that is 9888 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 103 is 9888.

LCM(96,103) = 9888

LCM of 96 and 103

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

LCM of:
and

Least Common Multiple of 96 and 103

LCM of 96 and 103 is 9888

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 103. First we will calculate the prime factors of 96 and 103.

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 103


103 103
1

Prime factors of 103 are 103. Prime factorization of 103 in exponential form is:

103 = 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 103.

LCM(96,103) = 25×31×1031
LCM(96,103) = 9888

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 103

List of positive integer factors of 103 that divides 103 without a remainder.

1, 103

Least Common Multiple of 96 and 103 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 103, than apply into the LCM equation.

GCF(96,103) = 1
LCM(96,103) = ( 96 × 103) / 1
LCM(96,103) = 9888 / 1
LCM(96,103) = 9888

Properties of LCM 96 and 103

(i) The LCM of 103 and 96 is associative

LCM of 96 and 103 = LCM of 103 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 103

Frequently Asked Questions on LCM of 96 and 103

1. What is the LCM of 96 and 103?

Answer: LCM of 96 and 103 is 9888.

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 103?

Answer: Factors of 103 are 1, 103. There are 2 integers that are factors of 103. The greatest factor of 103 is 103.

4. How to Find the LCM of 96 and 103?

Answer:

Least Common Multiple of 96 and 103 = 9888

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 103

103 = 103

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

LCM = 9888 = 2 x 2 x 2 x 2 x 2 x 3 x 103

Step 4: Therefore, the least common multiple of 96 and 103 is 9888.