Least Common Multiple of 172 and 180

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 172 and 180 the smallest integer that is 7740 that is divisible by both numbers.

Least Common Multiple (LCM) of 172 and 180 is 7740.

LCM(172,180) = 7740

LCM of 172 and 180

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

LCM of:
and

Least Common Multiple of 172 and 180

LCM of 172 and 180 is 7740

Least common multiple can be found by multiplying the highest exponent prime factors of 172 and 180. First we will calculate the prime factors of 172 and 180.

Prime Factorization of 172


2 172
2 86
43 43
1

Prime factors of 172 are 2,43. Prime factorization of 172 in exponential form is:

172 = 22×431

Prime Factorization of 180


2 180
2 90
3 45
3 15
5 5
1

Prime factors of 180 are 2, 3,5. Prime factorization of 180 in exponential form is:

180 = 22×32×51

Now multiplying the highest exponent prime factors to calculate the LCM of 172 and 180.

LCM(172,180) = 22×32×51×431
LCM(172,180) = 7740

Factors of 172

List of positive integer factors of 172 that divides 172 without a remainder.

1, 2, 4, 43, 86, 172

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Least Common Multiple of 172 and 180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 172 and 180, than apply into the LCM equation.

GCF(172,180) = 4
LCM(172,180) = ( 172 × 180) / 4
LCM(172,180) = 30960 / 4
LCM(172,180) = 7740

Properties of LCM 172 and 180

(i) The LCM of 180 and 172 is associative

LCM of 172 and 180 = LCM of 180 and 172

Related Least Common Multiples of 172

Related Least Common Multiples of 180

Frequently Asked Questions on LCM of 172 and 180

1. What is the LCM of 172 and 180?

Answer: LCM of 172 and 180 is 7740.

2. What are the Factors of 172?

Answer: Factors of 172 are 1, 2, 4, 43, 86, 172. There are 6 integers that are factors of 172. The greatest factor of 172 is 172.

3. What are the Factors of 180?

Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.

4. How to Find the LCM of 172 and 180?

Answer:

Least Common Multiple of 172 and 180 = 7740

Step 1: Find the prime factorization of 172

172 = 2 x 2 x 43

Step 2: Find the prime factorization of 180

180 = 2 x 2 x 3 x 3 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 = 7740 = 2 x 2 x 3 x 3 x 5 x 43

Step 4: Therefore, the least common multiple of 172 and 180 is 7740.