Least Common Multiple of 180 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 180 and 190 the smallest integer that is 3420 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 190 is 3420.

LCM(180,190) = 3420

LCM of 180 and 190

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

LCM of:
and

Least Common Multiple of 180 and 190

LCM of 180 and 190 is 3420

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 190. First we will calculate the prime factors of 180 and 190.

Prime Factorization of 180


2 180
2 90
3 45
3 15
5 5
1

Prime factors of 180 are 2, 3,5. Prime factorization of 180 in exponential form is:

180 = 22×32×51

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 180 and 190.

LCM(180,190) = 22×32×51×191
LCM(180,190) = 3420

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

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 180 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 180 and 190, than apply into the LCM equation.

GCF(180,190) = 10
LCM(180,190) = ( 180 × 190) / 10
LCM(180,190) = 34200 / 10
LCM(180,190) = 3420

Properties of LCM 180 and 190

(i) The LCM of 190 and 180 is associative

LCM of 180 and 190 = LCM of 190 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 190

Frequently Asked Questions on LCM of 180 and 190

1. What is the LCM of 180 and 190?

Answer: LCM of 180 and 190 is 3420.

2. What are the Factors of 180?

Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.

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 180 and 190?

Answer:

Least Common Multiple of 180 and 190 = 3420

Step 1: Find the prime factorization of 180

180 = 2 x 2 x 3 x 3 x 5

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 = 3420 = 2 x 2 x 3 x 3 x 5 x 19

Step 4: Therefore, the least common multiple of 180 and 190 is 3420.