Least Common Multiple of 177 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 177 and 180 the smallest integer that is 10620 that is divisible by both numbers.

Least Common Multiple (LCM) of 177 and 180 is 10620.

LCM(177,180) = 10620

LCM of 177 and 180

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

LCM of:
and

Least Common Multiple of 177 and 180

LCM of 177 and 180 is 10620

Least common multiple can be found by multiplying the highest exponent prime factors of 177 and 180. First we will calculate the prime factors of 177 and 180.

Prime Factorization of 177


3 177
59 59
1

Prime factors of 177 are 3,59. Prime factorization of 177 in exponential form is:

177 = 31×591

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 177 and 180.

LCM(177,180) = 22×32×51×591
LCM(177,180) = 10620

Factors of 177

List of positive integer factors of 177 that divides 177 without a remainder.

1, 3, 59, 177

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 177 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 177 and 180, than apply into the LCM equation.

GCF(177,180) = 3
LCM(177,180) = ( 177 × 180) / 3
LCM(177,180) = 31860 / 3
LCM(177,180) = 10620

Properties of LCM 177 and 180

(i) The LCM of 180 and 177 is associative

LCM of 177 and 180 = LCM of 180 and 177

Related Least Common Multiples of 177

Related Least Common Multiples of 180

Frequently Asked Questions on LCM of 177 and 180

1. What is the LCM of 177 and 180?

Answer: LCM of 177 and 180 is 10620.

2. What are the Factors of 177?

Answer: Factors of 177 are 1, 3, 59, 177. There are 4 integers that are factors of 177. The greatest factor of 177 is 177.

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 177 and 180?

Answer:

Least Common Multiple of 177 and 180 = 10620

Step 1: Find the prime factorization of 177

177 = 3 x 59

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 = 10620 = 2 x 2 x 3 x 3 x 5 x 59

Step 4: Therefore, the least common multiple of 177 and 180 is 10620.