Least Common Multiple of 102 and 106

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 102 and 106 the smallest integer that is 5406 that is divisible by both numbers.

Least Common Multiple (LCM) of 102 and 106 is 5406.

LCM(102,106) = 5406

LCM of 102 and 106

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

LCM of:
and

Least Common Multiple of 102 and 106

LCM of 102 and 106 is 5406

Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 106. First we will calculate the prime factors of 102 and 106.

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

Prime Factorization of 106


2 106
53 53
1

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 21×531

Now multiplying the highest exponent prime factors to calculate the LCM of 102 and 106.

LCM(102,106) = 21×31×171×531
LCM(102,106) = 5406

Factors of 102

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

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

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1, 2, 53, 106

Least Common Multiple of 102 and 106 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 102 and 106, than apply into the LCM equation.

GCF(102,106) = 2
LCM(102,106) = ( 102 × 106) / 2
LCM(102,106) = 10812 / 2
LCM(102,106) = 5406

Properties of LCM 102 and 106

(i) The LCM of 106 and 102 is associative

LCM of 102 and 106 = LCM of 106 and 102

Related Least Common Multiples of 102

Related Least Common Multiples of 106

Frequently Asked Questions on LCM of 102 and 106

1. What is the LCM of 102 and 106?

Answer: LCM of 102 and 106 is 5406.

2. 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.

3. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

4. How to Find the LCM of 102 and 106?

Answer:

Least Common Multiple of 102 and 106 = 5406

Step 1: Find the prime factorization of 102

102 = 2 x 3 x 17

Step 2: Find the prime factorization of 106

106 = 2 x 53

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

LCM = 5406 = 2 x 3 x 17 x 53

Step 4: Therefore, the least common multiple of 102 and 106 is 5406.