Least Common Multiple of 84 and 102

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 102 the smallest integer that is 1428 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 102 is 1428.

LCM(84,102) = 1428

LCM of 84 and 102

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

LCM of:
and

Least Common Multiple of 84 and 102

LCM of 84 and 102 is 1428

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 102. First we will calculate the prime factors of 84 and 102.

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 102


2 102
3 51
17 17
1

Prime factors of 102 are 2, 3,17. Prime factorization of 102 in exponential form is:

102 = 21×31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 102.

LCM(84,102) = 22×31×71×171
LCM(84,102) = 1428

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 102

List of positive integer factors of 102 that divides 102 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102

Least Common Multiple of 84 and 102 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 102, than apply into the LCM equation.

GCF(84,102) = 6
LCM(84,102) = ( 84 × 102) / 6
LCM(84,102) = 8568 / 6
LCM(84,102) = 1428

Properties of LCM 84 and 102

(i) The LCM of 102 and 84 is associative

LCM of 84 and 102 = LCM of 102 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 102

Frequently Asked Questions on LCM of 84 and 102

1. What is the LCM of 84 and 102?

Answer: LCM of 84 and 102 is 1428.

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 102?

Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.

4. How to Find the LCM of 84 and 102?

Answer:

Least Common Multiple of 84 and 102 = 1428

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 102

102 = 2 x 3 x 17

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

LCM = 1428 = 2 x 2 x 3 x 7 x 17

Step 4: Therefore, the least common multiple of 84 and 102 is 1428.