Least Common Multiple of 144 and 152

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 152 the smallest integer that is 2736 that is divisible by both numbers.

Least Common Multiple (LCM) of 144 and 152 is 2736.

LCM(144,152) = 2736

LCM of 144 and 152

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

LCM of:
and

Least Common Multiple of 144 and 152

LCM of 144 and 152 is 2736

Least common multiple can be found by multiplying the highest exponent prime factors of 144 and 152. First we will calculate the prime factors of 144 and 152.

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 152


2 152
2 76
2 38
19 19
1

Prime factors of 152 are 2,19. Prime factorization of 152 in exponential form is:

152 = 23×191

Now multiplying the highest exponent prime factors to calculate the LCM of 144 and 152.

LCM(144,152) = 24×32×191
LCM(144,152) = 2736

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 152

List of positive integer factors of 152 that divides 152 without a remainder.

1, 2, 4, 8, 19, 38, 76, 152

Least Common Multiple of 144 and 152 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 152, than apply into the LCM equation.

GCF(144,152) = 8
LCM(144,152) = ( 144 × 152) / 8
LCM(144,152) = 21888 / 8
LCM(144,152) = 2736

Properties of LCM 144 and 152

(i) The LCM of 152 and 144 is associative

LCM of 144 and 152 = LCM of 152 and 144

Related Least Common Multiples of 144

Related Least Common Multiples of 152

Frequently Asked Questions on LCM of 144 and 152

1. What is the LCM of 144 and 152?

Answer: LCM of 144 and 152 is 2736.

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 152?

Answer: Factors of 152 are 1, 2, 4, 8, 19, 38, 76, 152. There are 8 integers that are factors of 152. The greatest factor of 152 is 152.

4. How to Find the LCM of 144 and 152?

Answer:

Least Common Multiple of 144 and 152 = 2736

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 152

152 = 2 x 2 x 2 x 19

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

LCM = 2736 = 2 x 2 x 2 x 2 x 3 x 3 x 19

Step 4: Therefore, the least common multiple of 144 and 152 is 2736.