Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1203 and 1205 the smallest integer that is 1449615 that is divisible by both numbers.
Least Common Multiple (LCM) of 1203 and 1205 is 1449615.
LCM(1203,1205) = 1449615
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 1203 and 1205. First we will calculate the prime factors of 1203 and 1205.
Prime Factorization of 1203
3 | 1203 |
401 | 401 |
1 |
Prime factors of 1203 are 3,401. Prime factorization of 1203 in exponential form is:
1203 = 31×4011
Prime Factorization of 1205
5 | 1205 |
241 | 241 |
1 |
Prime factors of 1205 are 5,241. Prime factorization of 1205 in exponential form is:
1205 = 51×2411
Now multiplying the highest exponent prime factors to calculate the LCM of 1203 and 1205.
LCM(1203,1205) = 31×51×2411×4011
LCM(1203,1205) = 1449615
Factors of 1203
List of positive integer factors of 1203 that divides 1203 without a remainder.
1, 3, 401, 1203
Factors of 1205
List of positive integer factors of 1205 that divides 1205 without a remainder.
1, 5, 241, 1205
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1203 and 1205, than apply into the LCM equation.
GCF(1203,1205) = 1
LCM(1203,1205) = ( 1203 × 1205) / 1
LCM(1203,1205) = 1449615 / 1
LCM(1203,1205) = 1449615
(i) The LCM of 1205 and 1203 is associative
LCM of 1203 and 1205 = LCM of 1205 and 1203
1. What is the LCM of 1203 and 1205?
Answer: LCM of 1203 and 1205 is 1449615.
2. What are the Factors of 1203?
Answer: Factors of 1203 are 1, 3, 401, 1203. There are 4 integers that are factors of 1203. The greatest factor of 1203 is 1203.
3. What are the Factors of 1205?
Answer: Factors of 1205 are 1, 5, 241, 1205. There are 4 integers that are factors of 1205. The greatest factor of 1205 is 1205.
4. How to Find the LCM of 1203 and 1205?
Answer:
Least Common Multiple of 1203 and 1205 = 1449615
Step 1: Find the prime factorization of 1203
1203 = 3 x 401
Step 2: Find the prime factorization of 1205
1205 = 5 x 241
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1449615 = 3 x 5 x 241 x 401
Step 4: Therefore, the least common multiple of 1203 and 1205 is 1449615.