Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1208 and 1215 the smallest integer that is 1467720 that is divisible by both numbers.
Least Common Multiple (LCM) of 1208 and 1215 is 1467720.
LCM(1208,1215) = 1467720
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 1208 and 1215. First we will calculate the prime factors of 1208 and 1215.
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
Prime Factorization of 1215
3 | 1215 |
3 | 405 |
3 | 135 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 1215 are 3,5. Prime factorization of 1215 in exponential form is:
1215 = 35×51
Now multiplying the highest exponent prime factors to calculate the LCM of 1208 and 1215.
LCM(1208,1215) = 23×35×51×1511
LCM(1208,1215) = 1467720
Factors of 1208
List of positive integer factors of 1208 that divides 1208 without a remainder.
1, 2, 4, 8, 151, 302, 604, 1208
Factors of 1215
List of positive integer factors of 1215 that divides 1215 without a remainder.
1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1208 and 1215, than apply into the LCM equation.
GCF(1208,1215) = 1
LCM(1208,1215) = ( 1208 × 1215) / 1
LCM(1208,1215) = 1467720 / 1
LCM(1208,1215) = 1467720
(i) The LCM of 1215 and 1208 is associative
LCM of 1208 and 1215 = LCM of 1215 and 1208
1. What is the LCM of 1208 and 1215?
Answer: LCM of 1208 and 1215 is 1467720.
2. 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.
3. What are the Factors of 1215?
Answer: Factors of 1215 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215. There are 12 integers that are factors of 1215. The greatest factor of 1215 is 1215.
4. How to Find the LCM of 1208 and 1215?
Answer:
Least Common Multiple of 1208 and 1215 = 1467720
Step 1: Find the prime factorization of 1208
1208 = 2 x 2 x 2 x 151
Step 2: Find the prime factorization of 1215
1215 = 3 x 3 x 3 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1467720 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 151
Step 4: Therefore, the least common multiple of 1208 and 1215 is 1467720.