Least Common Multiple of 84 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 84 and 96 the smallest integer that is 672 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 96 is 672.

LCM(84,96) = 672

LCM of 84 and 96

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

LCM of:
and

Least Common Multiple of 84 and 96

LCM of 84 and 96 is 672

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 96. First we will calculate the prime factors of 84 and 96.

Prime Factorization of 84


2 84
2 42
3 21
7 7
1

Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

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 84 and 96.

LCM(84,96) = 25×31×71
LCM(84,96) = 672

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

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 84 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 84 and 96, than apply into the LCM equation.

GCF(84,96) = 12
LCM(84,96) = ( 84 × 96) / 12
LCM(84,96) = 8064 / 12
LCM(84,96) = 672

Properties of LCM 84 and 96

(i) The LCM of 96 and 84 is associative

LCM of 84 and 96 = LCM of 96 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 96

Frequently Asked Questions on LCM of 84 and 96

1. What is the LCM of 84 and 96?

Answer: LCM of 84 and 96 is 672.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

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 84 and 96?

Answer:

Least Common Multiple of 84 and 96 = 672

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

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 = 672 = 2 x 2 x 2 x 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 84 and 96 is 672.