Least Common Multiple of 165 and 171

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 165 and 171 the smallest integer that is 9405 that is divisible by both numbers.

Least Common Multiple (LCM) of 165 and 171 is 9405.

LCM(165,171) = 9405

LCM of 165 and 171

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

LCM of:
and

Least Common Multiple of 165 and 171

LCM of 165 and 171 is 9405

Least common multiple can be found by multiplying the highest exponent prime factors of 165 and 171. First we will calculate the prime factors of 165 and 171.

Prime Factorization of 165


3 165
5 55
11 11
1

Prime factors of 165 are 3, 5,11. Prime factorization of 165 in exponential form is:

165 = 31×51×111

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

Now multiplying the highest exponent prime factors to calculate the LCM of 165 and 171.

LCM(165,171) = 32×51×111×191
LCM(165,171) = 9405

Factors of 165

List of positive integer factors of 165 that divides 165 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165

Factors of 171

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

1, 3, 9, 19, 57, 171

Least Common Multiple of 165 and 171 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 165 and 171, than apply into the LCM equation.

GCF(165,171) = 3
LCM(165,171) = ( 165 × 171) / 3
LCM(165,171) = 28215 / 3
LCM(165,171) = 9405

Properties of LCM 165 and 171

(i) The LCM of 171 and 165 is associative

LCM of 165 and 171 = LCM of 171 and 165

Related Least Common Multiples of 165

Related Least Common Multiples of 171

Frequently Asked Questions on LCM of 165 and 171

1. What is the LCM of 165 and 171?

Answer: LCM of 165 and 171 is 9405.

2. What are the Factors of 165?

Answer: Factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165. There are 8 integers that are factors of 165. The greatest factor of 165 is 165.

3. 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.

4. How to Find the LCM of 165 and 171?

Answer:

Least Common Multiple of 165 and 171 = 9405

Step 1: Find the prime factorization of 165

165 = 3 x 5 x 11

Step 2: Find the prime factorization of 171

171 = 3 x 3 x 19

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

LCM = 9405 = 3 x 3 x 5 x 11 x 19

Step 4: Therefore, the least common multiple of 165 and 171 is 9405.