Least Common Multiple of 144 and 149

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 144 and 149 the smallest integer that is 21456 that is divisible by both numbers.

Least Common Multiple (LCM) of 144 and 149 is 21456.

LCM(144,149) = 21456

LCM of 144 and 149

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

LCM of:
and

Least Common Multiple of 144 and 149

LCM of 144 and 149 is 21456

Least common multiple can be found by multiplying the highest exponent prime factors of 144 and 149. First we will calculate the prime factors of 144 and 149.

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

Prime Factorization of 149


149 149
1

Prime factors of 149 are 149. Prime factorization of 149 in exponential form is:

149 = 1491

Now multiplying the highest exponent prime factors to calculate the LCM of 144 and 149.

LCM(144,149) = 24×32×1491
LCM(144,149) = 21456

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

Factors of 149

List of positive integer factors of 149 that divides 149 without a remainder.

1, 149

Least Common Multiple of 144 and 149 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 144 and 149, than apply into the LCM equation.

GCF(144,149) = 1
LCM(144,149) = ( 144 × 149) / 1
LCM(144,149) = 21456 / 1
LCM(144,149) = 21456

Properties of LCM 144 and 149

(i) The LCM of 149 and 144 is associative

LCM of 144 and 149 = LCM of 149 and 144

Related Least Common Multiples of 144

Related Least Common Multiples of 149

Frequently Asked Questions on LCM of 144 and 149

1. What is the LCM of 144 and 149?

Answer: LCM of 144 and 149 is 21456.

2. 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.

3. What are the Factors of 149?

Answer: Factors of 149 are 1, 149. There are 2 integers that are factors of 149. The greatest factor of 149 is 149.

4. How to Find the LCM of 144 and 149?

Answer:

Least Common Multiple of 144 and 149 = 21456

Step 1: Find the prime factorization of 144

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

Step 2: Find the prime factorization of 149

149 = 149

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

LCM = 21456 = 2 x 2 x 2 x 2 x 3 x 3 x 149

Step 4: Therefore, the least common multiple of 144 and 149 is 21456.