Least Common Multiple of 144 and 145

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 145 the smallest integer that is 20880 that is divisible by both numbers.

Least Common Multiple (LCM) of 144 and 145 is 20880.

LCM(144,145) = 20880

LCM of 144 and 145

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

LCM of:
and

Least Common Multiple of 144 and 145

LCM of 144 and 145 is 20880

Least common multiple can be found by multiplying the highest exponent prime factors of 144 and 145. First we will calculate the prime factors of 144 and 145.

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 145


5 145
29 29
1

Prime factors of 145 are 5,29. Prime factorization of 145 in exponential form is:

145 = 51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 144 and 145.

LCM(144,145) = 24×32×51×291
LCM(144,145) = 20880

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 145

List of positive integer factors of 145 that divides 145 without a remainder.

1, 5, 29, 145

Least Common Multiple of 144 and 145 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 145, than apply into the LCM equation.

GCF(144,145) = 1
LCM(144,145) = ( 144 × 145) / 1
LCM(144,145) = 20880 / 1
LCM(144,145) = 20880

Properties of LCM 144 and 145

(i) The LCM of 145 and 144 is associative

LCM of 144 and 145 = LCM of 145 and 144

Related Least Common Multiples of 144

Related Least Common Multiples of 145

Frequently Asked Questions on LCM of 144 and 145

1. What is the LCM of 144 and 145?

Answer: LCM of 144 and 145 is 20880.

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 145?

Answer: Factors of 145 are 1, 5, 29, 145. There are 4 integers that are factors of 145. The greatest factor of 145 is 145.

4. How to Find the LCM of 144 and 145?

Answer:

Least Common Multiple of 144 and 145 = 20880

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 145

145 = 5 x 29

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

LCM = 20880 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 144 and 145 is 20880.