Least Common Multiple of 171 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 171 and 178 the smallest integer that is 30438 that is divisible by both numbers.

Least Common Multiple (LCM) of 171 and 178 is 30438.

LCM(171,178) = 30438

LCM of 171 and 178

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

LCM of:
and

Least Common Multiple of 171 and 178

LCM of 171 and 178 is 30438

Least common multiple can be found by multiplying the highest exponent prime factors of 171 and 178. First we will calculate the prime factors of 171 and 178.

Prime Factorization of 171


3 171
3 57
19 19
1

Prime factors of 171 are 3,19. Prime factorization of 171 in exponential form is:

171 = 32×191

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 171 and 178.

LCM(171,178) = 21×32×191×891
LCM(171,178) = 30438

Factors of 171

List of positive integer factors of 171 that divides 171 without a remainder.

1, 3, 9, 19, 57, 171

Factors of 178

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

1, 2, 89, 178

Least Common Multiple of 171 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 171 and 178, than apply into the LCM equation.

GCF(171,178) = 1
LCM(171,178) = ( 171 × 178) / 1
LCM(171,178) = 30438 / 1
LCM(171,178) = 30438

Properties of LCM 171 and 178

(i) The LCM of 178 and 171 is associative

LCM of 171 and 178 = LCM of 178 and 171

Related Least Common Multiples of 171

Related Least Common Multiples of 178

Frequently Asked Questions on LCM of 171 and 178

1. What is the LCM of 171 and 178?

Answer: LCM of 171 and 178 is 30438.

2. What are the Factors of 171?

Answer: Factors of 171 are 1, 3, 9, 19, 57, 171. There are 6 integers that are factors of 171. The greatest factor of 171 is 171.

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 171 and 178?

Answer:

Least Common Multiple of 171 and 178 = 30438

Step 1: Find the prime factorization of 171

171 = 3 x 3 x 19

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 = 30438 = 2 x 3 x 3 x 19 x 89

Step 4: Therefore, the least common multiple of 171 and 178 is 30438.