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 1208 the smallest integer that is 1453224 that is divisible by both numbers.
Least Common Multiple (LCM) of 1203 and 1208 is 1453224.
LCM(1203,1208) = 1453224
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 1208. First we will calculate the prime factors of 1203 and 1208.
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 1208
2 | 1208 |
2 | 604 |
2 | 302 |
151 | 151 |
1 |
Prime factors of 1208 are 2,151. Prime factorization of 1208 in exponential form is:
1208 = 23×1511
Now multiplying the highest exponent prime factors to calculate the LCM of 1203 and 1208.
LCM(1203,1208) = 23×31×1511×4011
LCM(1203,1208) = 1453224
Factors of 1203
List of positive integer factors of 1203 that divides 1203 without a remainder.
1, 3, 401, 1203
Factors of 1208
List of positive integer factors of 1208 that divides 1208 without a remainder.
1, 2, 4, 8, 151, 302, 604, 1208
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1203 and 1208, than apply into the LCM equation.
GCF(1203,1208) = 1
LCM(1203,1208) = ( 1203 × 1208) / 1
LCM(1203,1208) = 1453224 / 1
LCM(1203,1208) = 1453224
(i) The LCM of 1208 and 1203 is associative
LCM of 1203 and 1208 = LCM of 1208 and 1203
1. What is the LCM of 1203 and 1208?
Answer: LCM of 1203 and 1208 is 1453224.
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 1208?
Answer: Factors of 1208 are 1, 2, 4, 8, 151, 302, 604, 1208. There are 8 integers that are factors of 1208. The greatest factor of 1208 is 1208.
4. How to Find the LCM of 1203 and 1208?
Answer:
Least Common Multiple of 1203 and 1208 = 1453224
Step 1: Find the prime factorization of 1203
1203 = 3 x 401
Step 2: Find the prime factorization of 1208
1208 = 2 x 2 x 2 x 151
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1453224 = 2 x 2 x 2 x 3 x 151 x 401
Step 4: Therefore, the least common multiple of 1203 and 1208 is 1453224.