Least Common Multiple of 144 and 150

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 150 the smallest integer that is 3600 that is divisible by both numbers.

Least Common Multiple (LCM) of 144 and 150 is 3600.

LCM(144,150) = 3600

LCM of 144 and 150

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

LCM of:
and

Least Common Multiple of 144 and 150

LCM of 144 and 150 is 3600

Least common multiple can be found by multiplying the highest exponent prime factors of 144 and 150. First we will calculate the prime factors of 144 and 150.

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 150


2 150
3 75
5 25
5 5
1

Prime factors of 150 are 2, 3,5. Prime factorization of 150 in exponential form is:

150 = 21×31×52

Now multiplying the highest exponent prime factors to calculate the LCM of 144 and 150.

LCM(144,150) = 24×32×52
LCM(144,150) = 3600

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 150

List of positive integer factors of 150 that divides 150 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Least Common Multiple of 144 and 150 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 150, than apply into the LCM equation.

GCF(144,150) = 6
LCM(144,150) = ( 144 × 150) / 6
LCM(144,150) = 21600 / 6
LCM(144,150) = 3600

Properties of LCM 144 and 150

(i) The LCM of 150 and 144 is associative

LCM of 144 and 150 = LCM of 150 and 144

Related Least Common Multiples of 144

Related Least Common Multiples of 150

Frequently Asked Questions on LCM of 144 and 150

1. What is the LCM of 144 and 150?

Answer: LCM of 144 and 150 is 3600.

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 150?

Answer: Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150. There are 12 integers that are factors of 150. The greatest factor of 150 is 150.

4. How to Find the LCM of 144 and 150?

Answer:

Least Common Multiple of 144 and 150 = 3600

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 150

150 = 2 x 3 x 5 x 5

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

LCM = 3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 144 and 150 is 3600.