Least Common Multiple of 189 and 196

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 196 the smallest integer that is 5292 that is divisible by both numbers.

Least Common Multiple (LCM) of 189 and 196 is 5292.

LCM(189,196) = 5292

LCM of 189 and 196

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

LCM of:
and

Least Common Multiple of 189 and 196

LCM of 189 and 196 is 5292

Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 196. First we will calculate the prime factors of 189 and 196.

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 196


2 196
2 98
7 49
7 7
1

Prime factors of 196 are 2,7. Prime factorization of 196 in exponential form is:

196 = 22×72

Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 196.

LCM(189,196) = 22×33×72
LCM(189,196) = 5292

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 196

List of positive integer factors of 196 that divides 196 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196

Least Common Multiple of 189 and 196 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 196, than apply into the LCM equation.

GCF(189,196) = 7
LCM(189,196) = ( 189 × 196) / 7
LCM(189,196) = 37044 / 7
LCM(189,196) = 5292

Properties of LCM 189 and 196

(i) The LCM of 196 and 189 is associative

LCM of 189 and 196 = LCM of 196 and 189

Related Least Common Multiples of 189

Related Least Common Multiples of 196

Frequently Asked Questions on LCM of 189 and 196

1. What is the LCM of 189 and 196?

Answer: LCM of 189 and 196 is 5292.

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 196?

Answer: Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. There are 9 integers that are factors of 196. The greatest factor of 196 is 196.

4. How to Find the LCM of 189 and 196?

Answer:

Least Common Multiple of 189 and 196 = 5292

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 196

196 = 2 x 2 x 7 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 = 5292 = 2 x 2 x 3 x 3 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 189 and 196 is 5292.