Least Common Multiple of 96 and 105

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 105 the smallest integer that is 3360 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 105 is 3360.

LCM(96,105) = 3360

LCM of 96 and 105

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

LCM of:
and

Least Common Multiple of 96 and 105

LCM of 96 and 105 is 3360

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 105. First we will calculate the prime factors of 96 and 105.

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 105


3 105
5 35
7 7
1

Prime factors of 105 are 3, 5,7. Prime factorization of 105 in exponential form is:

105 = 31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 105.

LCM(96,105) = 25×31×51×71
LCM(96,105) = 3360

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 105

List of positive integer factors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105

Least Common Multiple of 96 and 105 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 105, than apply into the LCM equation.

GCF(96,105) = 3
LCM(96,105) = ( 96 × 105) / 3
LCM(96,105) = 10080 / 3
LCM(96,105) = 3360

Properties of LCM 96 and 105

(i) The LCM of 105 and 96 is associative

LCM of 96 and 105 = LCM of 105 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 105

Frequently Asked Questions on LCM of 96 and 105

1. What is the LCM of 96 and 105?

Answer: LCM of 96 and 105 is 3360.

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 105?

Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.

4. How to Find the LCM of 96 and 105?

Answer:

Least Common Multiple of 96 and 105 = 3360

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 105

105 = 3 x 5 x 7

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

LCM = 3360 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 96 and 105 is 3360.