Least Common Multiple of 138 and 140

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 140 the smallest integer that is 9660 that is divisible by both numbers.

Least Common Multiple (LCM) of 138 and 140 is 9660.

LCM(138,140) = 9660

LCM of 138 and 140

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

LCM of:
and

Least Common Multiple of 138 and 140

LCM of 138 and 140 is 9660

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 140. First we will calculate the prime factors of 138 and 140.

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 140


2 140
2 70
5 35
7 7
1

Prime factors of 140 are 2, 5,7. Prime factorization of 140 in exponential form is:

140 = 22×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 140.

LCM(138,140) = 22×31×51×71×231
LCM(138,140) = 9660

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 140

List of positive integer factors of 140 that divides 140 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

Least Common Multiple of 138 and 140 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 140, than apply into the LCM equation.

GCF(138,140) = 2
LCM(138,140) = ( 138 × 140) / 2
LCM(138,140) = 19320 / 2
LCM(138,140) = 9660

Properties of LCM 138 and 140

(i) The LCM of 140 and 138 is associative

LCM of 138 and 140 = LCM of 140 and 138

Related Least Common Multiples of 138

Related Least Common Multiples of 140

Frequently Asked Questions on LCM of 138 and 140

1. What is the LCM of 138 and 140?

Answer: LCM of 138 and 140 is 9660.

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 140?

Answer: Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. There are 12 integers that are factors of 140. The greatest factor of 140 is 140.

4. How to Find the LCM of 138 and 140?

Answer:

Least Common Multiple of 138 and 140 = 9660

Step 1: Find the prime factorization of 138

138 = 2 x 3 x 23

Step 2: Find the prime factorization of 140

140 = 2 x 2 x 5 x 7

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

LCM = 9660 = 2 x 2 x 3 x 5 x 7 x 23

Step 4: Therefore, the least common multiple of 138 and 140 is 9660.