Least Common Multiple of 172 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 172 and 178 the smallest integer that is 15308 that is divisible by both numbers.

Least Common Multiple (LCM) of 172 and 178 is 15308.

LCM(172,178) = 15308

LCM of 172 and 178

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

LCM of:
and

Least Common Multiple of 172 and 178

LCM of 172 and 178 is 15308

Least common multiple can be found by multiplying the highest exponent prime factors of 172 and 178. First we will calculate the prime factors of 172 and 178.

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 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 172 and 178.

LCM(172,178) = 22×431×891
LCM(172,178) = 15308

Factors of 172

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

1, 2, 4, 43, 86, 172

Factors of 178

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

1, 2, 89, 178

Least Common Multiple of 172 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 172 and 178, than apply into the LCM equation.

GCF(172,178) = 2
LCM(172,178) = ( 172 × 178) / 2
LCM(172,178) = 30616 / 2
LCM(172,178) = 15308

Properties of LCM 172 and 178

(i) The LCM of 178 and 172 is associative

LCM of 172 and 178 = LCM of 178 and 172

Related Least Common Multiples of 172

Related Least Common Multiples of 178

Frequently Asked Questions on LCM of 172 and 178

1. What is the LCM of 172 and 178?

Answer: LCM of 172 and 178 is 15308.

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 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 172 and 178?

Answer:

Least Common Multiple of 172 and 178 = 15308

Step 1: Find the prime factorization of 172

172 = 2 x 2 x 43

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 = 15308 = 2 x 2 x 43 x 89

Step 4: Therefore, the least common multiple of 172 and 178 is 15308.