Least Common Multiple of 102 and 104

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 104 the smallest integer that is 5304 that is divisible by both numbers.

Least Common Multiple (LCM) of 102 and 104 is 5304.

LCM(102,104) = 5304

LCM of 102 and 104

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

LCM of:
and

Least Common Multiple of 102 and 104

LCM of 102 and 104 is 5304

Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 104. First we will calculate the prime factors of 102 and 104.

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 104


2 104
2 52
2 26
13 13
1

Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:

104 = 23×131

Now multiplying the highest exponent prime factors to calculate the LCM of 102 and 104.

LCM(102,104) = 23×31×131×171
LCM(102,104) = 5304

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 104

List of positive integer factors of 104 that divides 104 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104

Least Common Multiple of 102 and 104 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 104, than apply into the LCM equation.

GCF(102,104) = 2
LCM(102,104) = ( 102 × 104) / 2
LCM(102,104) = 10608 / 2
LCM(102,104) = 5304

Properties of LCM 102 and 104

(i) The LCM of 104 and 102 is associative

LCM of 102 and 104 = LCM of 104 and 102

Related Least Common Multiples of 102

Related Least Common Multiples of 104

Frequently Asked Questions on LCM of 102 and 104

1. What is the LCM of 102 and 104?

Answer: LCM of 102 and 104 is 5304.

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 104?

Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.

4. How to Find the LCM of 102 and 104?

Answer:

Least Common Multiple of 102 and 104 = 5304

Step 1: Find the prime factorization of 102

102 = 2 x 3 x 17

Step 2: Find the prime factorization of 104

104 = 2 x 2 x 2 x 13

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

LCM = 5304 = 2 x 2 x 2 x 3 x 13 x 17

Step 4: Therefore, the least common multiple of 102 and 104 is 5304.