Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 203 and 204 the smallest integer that is 41412 that is divisible by both numbers.
Least Common Multiple (LCM) of 203 and 204 is 41412.
LCM(203,204) = 41412
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 203 and 204. First we will calculate the prime factors of 203 and 204.
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
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 203 and 204.
LCM(203,204) = 22×31×71×171×291
LCM(203,204) = 41412
Factors of 203
List of positive integer factors of 203 that divides 203 without a remainder.
1, 7, 29, 203
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 203 and 204, than apply into the LCM equation.
GCF(203,204) = 1
LCM(203,204) = ( 203 × 204) / 1
LCM(203,204) = 41412 / 1
LCM(203,204) = 41412
(i) The LCM of 204 and 203 is associative
LCM of 203 and 204 = LCM of 204 and 203
1. What is the LCM of 203 and 204?
Answer: LCM of 203 and 204 is 41412.
2. 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.
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 203 and 204?
Answer:
Least Common Multiple of 203 and 204 = 41412
Step 1: Find the prime factorization of 203
203 = 7 x 29
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 = 41412 = 2 x 2 x 3 x 7 x 17 x 29
Step 4: Therefore, the least common multiple of 203 and 204 is 41412.