Least Common Multiple of 140 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 140 and 144 the smallest integer that is 5040 that is divisible by both numbers.

Least Common Multiple (LCM) of 140 and 144 is 5040.

LCM(140,144) = 5040

LCM of 140 and 144

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

LCM of:
and

Least Common Multiple of 140 and 144

LCM of 140 and 144 is 5040

Least common multiple can be found by multiplying the highest exponent prime factors of 140 and 144. First we will calculate the prime factors of 140 and 144.

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

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 140 and 144.

LCM(140,144) = 24×32×51×71
LCM(140,144) = 5040

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

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 140 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 140 and 144, than apply into the LCM equation.

GCF(140,144) = 4
LCM(140,144) = ( 140 × 144) / 4
LCM(140,144) = 20160 / 4
LCM(140,144) = 5040

Properties of LCM 140 and 144

(i) The LCM of 144 and 140 is associative

LCM of 140 and 144 = LCM of 144 and 140

Related Least Common Multiples of 140

Related Least Common Multiples of 144

Frequently Asked Questions on LCM of 140 and 144

1. What is the LCM of 140 and 144?

Answer: LCM of 140 and 144 is 5040.

2. 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.

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 140 and 144?

Answer:

Least Common Multiple of 140 and 144 = 5040

Step 1: Find the prime factorization of 140

140 = 2 x 2 x 5 x 7

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 = 5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 140 and 144 is 5040.