Least Common Multiple of 186 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 186 and 189 the smallest integer that is 11718 that is divisible by both numbers.

Least Common Multiple (LCM) of 186 and 189 is 11718.

LCM(186,189) = 11718

LCM of 186 and 189

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

LCM of:
and

Least Common Multiple of 186 and 189

LCM of 186 and 189 is 11718

Least common multiple can be found by multiplying the highest exponent prime factors of 186 and 189. First we will calculate the prime factors of 186 and 189.

Prime Factorization of 186


2 186
3 93
31 31
1

Prime factors of 186 are 2, 3,31. Prime factorization of 186 in exponential form is:

186 = 21×31×311

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 186 and 189.

LCM(186,189) = 21×33×71×311
LCM(186,189) = 11718

Factors of 186

List of positive integer factors of 186 that divides 186 without a remainder.

1, 2, 3, 6, 31, 62, 93, 186

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 186 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 186 and 189, than apply into the LCM equation.

GCF(186,189) = 3
LCM(186,189) = ( 186 × 189) / 3
LCM(186,189) = 35154 / 3
LCM(186,189) = 11718

Properties of LCM 186 and 189

(i) The LCM of 189 and 186 is associative

LCM of 186 and 189 = LCM of 189 and 186

Related Least Common Multiples of 186

Related Least Common Multiples of 189

Frequently Asked Questions on LCM of 186 and 189

1. What is the LCM of 186 and 189?

Answer: LCM of 186 and 189 is 11718.

2. What are the Factors of 186?

Answer: Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186. There are 8 integers that are factors of 186. The greatest factor of 186 is 186.

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 186 and 189?

Answer:

Least Common Multiple of 186 and 189 = 11718

Step 1: Find the prime factorization of 186

186 = 2 x 3 x 31

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 = 11718 = 2 x 3 x 3 x 3 x 7 x 31

Step 4: Therefore, the least common multiple of 186 and 189 is 11718.