Least Common Multiple of 138 and 142

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 138 and 142 the smallest integer that is 9798 that is divisible by both numbers.

Least Common Multiple (LCM) of 138 and 142 is 9798.

LCM(138,142) = 9798

LCM of 138 and 142

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

LCM of:
and

Least Common Multiple of 138 and 142

LCM of 138 and 142 is 9798

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 142. First we will calculate the prime factors of 138 and 142.

Prime Factorization of 138


2 138
3 69
23 23
1

Prime factors of 138 are 2, 3,23. Prime factorization of 138 in exponential form is:

138 = 21×31×231

Prime Factorization of 142


2 142
71 71
1

Prime factors of 142 are 2,71. Prime factorization of 142 in exponential form is:

142 = 21×711

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 142.

LCM(138,142) = 21×31×231×711
LCM(138,142) = 9798

Factors of 138

List of positive integer factors of 138 that divides 138 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138

Factors of 142

List of positive integer factors of 142 that divides 142 without a remainder.

1, 2, 71, 142

Least Common Multiple of 138 and 142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 138 and 142, than apply into the LCM equation.

GCF(138,142) = 2
LCM(138,142) = ( 138 × 142) / 2
LCM(138,142) = 19596 / 2
LCM(138,142) = 9798

Properties of LCM 138 and 142

(i) The LCM of 142 and 138 is associative

LCM of 138 and 142 = LCM of 142 and 138

Related Least Common Multiples of 138

Related Least Common Multiples of 142

Frequently Asked Questions on LCM of 138 and 142

1. What is the LCM of 138 and 142?

Answer: LCM of 138 and 142 is 9798.

2. What are the Factors of 138?

Answer: Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138. There are 8 integers that are factors of 138. The greatest factor of 138 is 138.

3. What are the Factors of 142?

Answer: Factors of 142 are 1, 2, 71, 142. There are 4 integers that are factors of 142. The greatest factor of 142 is 142.

4. How to Find the LCM of 138 and 142?

Answer:

Least Common Multiple of 138 and 142 = 9798

Step 1: Find the prime factorization of 138

138 = 2 x 3 x 23

Step 2: Find the prime factorization of 142

142 = 2 x 71

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

LCM = 9798 = 2 x 3 x 23 x 71

Step 4: Therefore, the least common multiple of 138 and 142 is 9798.