Least Common Multiple of 165 and 172

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 172 the smallest integer that is 28380 that is divisible by both numbers.

Least Common Multiple (LCM) of 165 and 172 is 28380.

LCM(165,172) = 28380

LCM of 165 and 172

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

LCM of:
and

Least Common Multiple of 165 and 172

LCM of 165 and 172 is 28380

Least common multiple can be found by multiplying the highest exponent prime factors of 165 and 172. First we will calculate the prime factors of 165 and 172.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 165 and 172.

LCM(165,172) = 22×31×51×111×431
LCM(165,172) = 28380

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 172

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

1, 2, 4, 43, 86, 172

Least Common Multiple of 165 and 172 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 172, than apply into the LCM equation.

GCF(165,172) = 1
LCM(165,172) = ( 165 × 172) / 1
LCM(165,172) = 28380 / 1
LCM(165,172) = 28380

Properties of LCM 165 and 172

(i) The LCM of 172 and 165 is associative

LCM of 165 and 172 = LCM of 172 and 165

Related Least Common Multiples of 165

Related Least Common Multiples of 172

Frequently Asked Questions on LCM of 165 and 172

1. What is the LCM of 165 and 172?

Answer: LCM of 165 and 172 is 28380.

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 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.

4. How to Find the LCM of 165 and 172?

Answer:

Least Common Multiple of 165 and 172 = 28380

Step 1: Find the prime factorization of 165

165 = 3 x 5 x 11

Step 2: Find the prime factorization of 172

172 = 2 x 2 x 43

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

LCM = 28380 = 2 x 2 x 3 x 5 x 11 x 43

Step 4: Therefore, the least common multiple of 165 and 172 is 28380.