Least Common Multiple of 176 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 176 and 180 the smallest integer that is 7920 that is divisible by both numbers.

Least Common Multiple (LCM) of 176 and 180 is 7920.

LCM(176,180) = 7920

LCM of 176 and 180

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

LCM of:
and

Least Common Multiple of 176 and 180

LCM of 176 and 180 is 7920

Least common multiple can be found by multiplying the highest exponent prime factors of 176 and 180. First we will calculate the prime factors of 176 and 180.

Prime Factorization of 176


2 176
2 88
2 44
2 22
11 11
1

Prime factors of 176 are 2,11. Prime factorization of 176 in exponential form is:

176 = 24×111

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 176 and 180.

LCM(176,180) = 24×32×51×111
LCM(176,180) = 7920

Factors of 176

List of positive integer factors of 176 that divides 176 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176

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 176 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 176 and 180, than apply into the LCM equation.

GCF(176,180) = 4
LCM(176,180) = ( 176 × 180) / 4
LCM(176,180) = 31680 / 4
LCM(176,180) = 7920

Properties of LCM 176 and 180

(i) The LCM of 180 and 176 is associative

LCM of 176 and 180 = LCM of 180 and 176

Related Least Common Multiples of 176

Related Least Common Multiples of 180

Frequently Asked Questions on LCM of 176 and 180

1. What is the LCM of 176 and 180?

Answer: LCM of 176 and 180 is 7920.

2. What are the Factors of 176?

Answer: Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. There are 10 integers that are factors of 176. The greatest factor of 176 is 176.

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 176 and 180?

Answer:

Least Common Multiple of 176 and 180 = 7920

Step 1: Find the prime factorization of 176

176 = 2 x 2 x 2 x 2 x 11

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 = 7920 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 176 and 180 is 7920.