Least Common Multiple of 177 and 178

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 178 the smallest integer that is 31506 that is divisible by both numbers.

Least Common Multiple (LCM) of 177 and 178 is 31506.

LCM(177,178) = 31506

LCM of 177 and 178

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

LCM of:
and

Least Common Multiple of 177 and 178

LCM of 177 and 178 is 31506

Least common multiple can be found by multiplying the highest exponent prime factors of 177 and 178. First we will calculate the prime factors of 177 and 178.

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 178


2 178
89 89
1

Prime factors of 178 are 2,89. Prime factorization of 178 in exponential form is:

178 = 21×891

Now multiplying the highest exponent prime factors to calculate the LCM of 177 and 178.

LCM(177,178) = 21×31×591×891
LCM(177,178) = 31506

Factors of 177

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

1, 3, 59, 177

Factors of 178

List of positive integer factors of 178 that divides 178 without a remainder.

1, 2, 89, 178

Least Common Multiple of 177 and 178 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 178, than apply into the LCM equation.

GCF(177,178) = 1
LCM(177,178) = ( 177 × 178) / 1
LCM(177,178) = 31506 / 1
LCM(177,178) = 31506

Properties of LCM 177 and 178

(i) The LCM of 178 and 177 is associative

LCM of 177 and 178 = LCM of 178 and 177

Related Least Common Multiples of 177

Related Least Common Multiples of 178

Frequently Asked Questions on LCM of 177 and 178

1. What is the LCM of 177 and 178?

Answer: LCM of 177 and 178 is 31506.

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 178?

Answer: Factors of 178 are 1, 2, 89, 178. There are 4 integers that are factors of 178. The greatest factor of 178 is 178.

4. How to Find the LCM of 177 and 178?

Answer:

Least Common Multiple of 177 and 178 = 31506

Step 1: Find the prime factorization of 177

177 = 3 x 59

Step 2: Find the prime factorization of 178

178 = 2 x 89

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

LCM = 31506 = 2 x 3 x 59 x 89

Step 4: Therefore, the least common multiple of 177 and 178 is 31506.