Least Common Multiple of 138 and 144

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 144 the smallest integer that is 3312 that is divisible by both numbers.

Least Common Multiple (LCM) of 138 and 144 is 3312.

LCM(138,144) = 3312

LCM of 138 and 144

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

LCM of:
and

Least Common Multiple of 138 and 144

LCM of 138 and 144 is 3312

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 144. First we will calculate the prime factors of 138 and 144.

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 144


2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 144 are 2,3. Prime factorization of 144 in exponential form is:

144 = 24×32

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 144.

LCM(138,144) = 24×32×231
LCM(138,144) = 3312

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 144

List of positive integer factors of 144 that divides 144 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Least Common Multiple of 138 and 144 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 144, than apply into the LCM equation.

GCF(138,144) = 6
LCM(138,144) = ( 138 × 144) / 6
LCM(138,144) = 19872 / 6
LCM(138,144) = 3312

Properties of LCM 138 and 144

(i) The LCM of 144 and 138 is associative

LCM of 138 and 144 = LCM of 144 and 138

Related Least Common Multiples of 138

Related Least Common Multiples of 144

Frequently Asked Questions on LCM of 138 and 144

1. What is the LCM of 138 and 144?

Answer: LCM of 138 and 144 is 3312.

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 144?

Answer: Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. There are 15 integers that are factors of 144. The greatest factor of 144 is 144.

4. How to Find the LCM of 138 and 144?

Answer:

Least Common Multiple of 138 and 144 = 3312

Step 1: Find the prime factorization of 138

138 = 2 x 3 x 23

Step 2: Find the prime factorization of 144

144 = 2 x 2 x 2 x 2 x 3 x 3

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

LCM = 3312 = 2 x 2 x 2 x 2 x 3 x 3 x 23

Step 4: Therefore, the least common multiple of 138 and 144 is 3312.