Least Common Multiple of 138 and 146

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 146 the smallest integer that is 10074 that is divisible by both numbers.

Least Common Multiple (LCM) of 138 and 146 is 10074.

LCM(138,146) = 10074

LCM of 138 and 146

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

LCM of:
and

Least Common Multiple of 138 and 146

LCM of 138 and 146 is 10074

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 146. First we will calculate the prime factors of 138 and 146.

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 146


2 146
73 73
1

Prime factors of 146 are 2,73. Prime factorization of 146 in exponential form is:

146 = 21×731

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 146.

LCM(138,146) = 21×31×231×731
LCM(138,146) = 10074

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 146

List of positive integer factors of 146 that divides 146 without a remainder.

1, 2, 73, 146

Least Common Multiple of 138 and 146 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 146, than apply into the LCM equation.

GCF(138,146) = 2
LCM(138,146) = ( 138 × 146) / 2
LCM(138,146) = 20148 / 2
LCM(138,146) = 10074

Properties of LCM 138 and 146

(i) The LCM of 146 and 138 is associative

LCM of 138 and 146 = LCM of 146 and 138

Related Least Common Multiples of 138

Related Least Common Multiples of 146

Frequently Asked Questions on LCM of 138 and 146

1. What is the LCM of 138 and 146?

Answer: LCM of 138 and 146 is 10074.

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 146?

Answer: Factors of 146 are 1, 2, 73, 146. There are 4 integers that are factors of 146. The greatest factor of 146 is 146.

4. How to Find the LCM of 138 and 146?

Answer:

Least Common Multiple of 138 and 146 = 10074

Step 1: Find the prime factorization of 138

138 = 2 x 3 x 23

Step 2: Find the prime factorization of 146

146 = 2 x 73

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

LCM = 10074 = 2 x 3 x 23 x 73

Step 4: Therefore, the least common multiple of 138 and 146 is 10074.