Least Common Multiple of 196 and 204

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 196 and 204 the smallest integer that is 9996 that is divisible by both numbers.

Least Common Multiple (LCM) of 196 and 204 is 9996.

LCM(196,204) = 9996

LCM of 196 and 204

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

LCM of:
and

Least Common Multiple of 196 and 204

LCM of 196 and 204 is 9996

Least common multiple can be found by multiplying the highest exponent prime factors of 196 and 204. First we will calculate the prime factors of 196 and 204.

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

Prime Factorization of 204


2 204
2 102
3 51
17 17
1

Prime factors of 204 are 2, 3,17. Prime factorization of 204 in exponential form is:

204 = 22×31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 196 and 204.

LCM(196,204) = 22×31×72×171
LCM(196,204) = 9996

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

Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

Least Common Multiple of 196 and 204 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 196 and 204, than apply into the LCM equation.

GCF(196,204) = 4
LCM(196,204) = ( 196 × 204) / 4
LCM(196,204) = 39984 / 4
LCM(196,204) = 9996

Properties of LCM 196 and 204

(i) The LCM of 204 and 196 is associative

LCM of 196 and 204 = LCM of 204 and 196

Related Least Common Multiples of 196

Related Least Common Multiples of 204

Frequently Asked Questions on LCM of 196 and 204

1. What is the LCM of 196 and 204?

Answer: LCM of 196 and 204 is 9996.

2. 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.

3. What are the Factors of 204?

Answer: Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. There are 12 integers that are factors of 204. The greatest factor of 204 is 204.

4. How to Find the LCM of 196 and 204?

Answer:

Least Common Multiple of 196 and 204 = 9996

Step 1: Find the prime factorization of 196

196 = 2 x 2 x 7 x 7

Step 2: Find the prime factorization of 204

204 = 2 x 2 x 3 x 17

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

LCM = 9996 = 2 x 2 x 3 x 7 x 7 x 17

Step 4: Therefore, the least common multiple of 196 and 204 is 9996.