Least Common Multiple of 198 and 203

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 198 and 203 the smallest integer that is 40194 that is divisible by both numbers.

Least Common Multiple (LCM) of 198 and 203 is 40194.

LCM(198,203) = 40194

LCM of 198 and 203

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

LCM of:
and

Least Common Multiple of 198 and 203

LCM of 198 and 203 is 40194

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 203. First we will calculate the prime factors of 198 and 203.

Prime Factorization of 198


2 198
3 99
3 33
11 11
1

Prime factors of 198 are 2, 3,11. Prime factorization of 198 in exponential form is:

198 = 21×32×111

Prime Factorization of 203


7 203
29 29
1

Prime factors of 203 are 7,29. Prime factorization of 203 in exponential form is:

203 = 71×291

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 203.

LCM(198,203) = 21×32×71×111×291
LCM(198,203) = 40194

Factors of 198

List of positive integer factors of 198 that divides 198 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

Factors of 203

List of positive integer factors of 203 that divides 203 without a remainder.

1, 7, 29, 203

Least Common Multiple of 198 and 203 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 198 and 203, than apply into the LCM equation.

GCF(198,203) = 1
LCM(198,203) = ( 198 × 203) / 1
LCM(198,203) = 40194 / 1
LCM(198,203) = 40194

Properties of LCM 198 and 203

(i) The LCM of 203 and 198 is associative

LCM of 198 and 203 = LCM of 203 and 198

Related Least Common Multiples of 198

Related Least Common Multiples of 203

Frequently Asked Questions on LCM of 198 and 203

1. What is the LCM of 198 and 203?

Answer: LCM of 198 and 203 is 40194.

2. What are the Factors of 198?

Answer: Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. There are 12 integers that are factors of 198. The greatest factor of 198 is 198.

3. What are the Factors of 203?

Answer: Factors of 203 are 1, 7, 29, 203. There are 4 integers that are factors of 203. The greatest factor of 203 is 203.

4. How to Find the LCM of 198 and 203?

Answer:

Least Common Multiple of 198 and 203 = 40194

Step 1: Find the prime factorization of 198

198 = 2 x 3 x 3 x 11

Step 2: Find the prime factorization of 203

203 = 7 x 29

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

LCM = 40194 = 2 x 3 x 3 x 7 x 11 x 29

Step 4: Therefore, the least common multiple of 198 and 203 is 40194.