Least Common Multiple of 189 and 190

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 189 and 190 the smallest integer that is 35910 that is divisible by both numbers.

Least Common Multiple (LCM) of 189 and 190 is 35910.

LCM(189,190) = 35910

LCM of 189 and 190

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

LCM of:
and

Least Common Multiple of 189 and 190

LCM of 189 and 190 is 35910

Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 190. First we will calculate the prime factors of 189 and 190.

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

Prime Factorization of 190


2 190
5 95
19 19
1

Prime factors of 190 are 2, 5,19. Prime factorization of 190 in exponential form is:

190 = 21×51×191

Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 190.

LCM(189,190) = 21×33×51×71×191
LCM(189,190) = 35910

Factors of 189

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

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

Factors of 190

List of positive integer factors of 190 that divides 190 without a remainder.

1, 2, 5, 10, 19, 38, 95, 190

Least Common Multiple of 189 and 190 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 189 and 190, than apply into the LCM equation.

GCF(189,190) = 1
LCM(189,190) = ( 189 × 190) / 1
LCM(189,190) = 35910 / 1
LCM(189,190) = 35910

Properties of LCM 189 and 190

(i) The LCM of 190 and 189 is associative

LCM of 189 and 190 = LCM of 190 and 189

Related Least Common Multiples of 189

Related Least Common Multiples of 190

Frequently Asked Questions on LCM of 189 and 190

1. What is the LCM of 189 and 190?

Answer: LCM of 189 and 190 is 35910.

2. 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.

3. What are the Factors of 190?

Answer: Factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190. There are 8 integers that are factors of 190. The greatest factor of 190 is 190.

4. How to Find the LCM of 189 and 190?

Answer:

Least Common Multiple of 189 and 190 = 35910

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 190

190 = 2 x 5 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 = 35910 = 2 x 3 x 3 x 3 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 189 and 190 is 35910.