Least Common Multiple of 185 and 189

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 185 and 189 the smallest integer that is 34965 that is divisible by both numbers.

Least Common Multiple (LCM) of 185 and 189 is 34965.

LCM(185,189) = 34965

LCM of 185 and 189

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

LCM of:
and

Least Common Multiple of 185 and 189

LCM of 185 and 189 is 34965

Least common multiple can be found by multiplying the highest exponent prime factors of 185 and 189. First we will calculate the prime factors of 185 and 189.

Prime Factorization of 185


5 185
37 37
1

Prime factors of 185 are 5,37. Prime factorization of 185 in exponential form is:

185 = 51×371

Prime Factorization of 189


3 189
3 63
3 21
7 7
1

Prime factors of 189 are 3,7. Prime factorization of 189 in exponential form is:

189 = 33×71

Now multiplying the highest exponent prime factors to calculate the LCM of 185 and 189.

LCM(185,189) = 33×51×71×371
LCM(185,189) = 34965

Factors of 185

List of positive integer factors of 185 that divides 185 without a remainder.

1, 5, 37, 185

Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63, 189

Least Common Multiple of 185 and 189 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 185 and 189, than apply into the LCM equation.

GCF(185,189) = 1
LCM(185,189) = ( 185 × 189) / 1
LCM(185,189) = 34965 / 1
LCM(185,189) = 34965

Properties of LCM 185 and 189

(i) The LCM of 189 and 185 is associative

LCM of 185 and 189 = LCM of 189 and 185

Frequently Asked Questions on LCM of 185 and 189

1. What is the LCM of 185 and 189?

Answer: LCM of 185 and 189 is 34965.

2. What are the Factors of 185?

Answer: Factors of 185 are 1, 5, 37, 185. There are 4 integers that are factors of 185. The greatest factor of 185 is 185.

3. What are the Factors of 189?

Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.

4. How to Find the LCM of 185 and 189?

Answer:

Least Common Multiple of 185 and 189 = 34965

Step 1: Find the prime factorization of 185

185 = 5 x 37

Step 2: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

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

LCM = 34965 = 3 x 3 x 3 x 5 x 7 x 37

Step 4: Therefore, the least common multiple of 185 and 189 is 34965.