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 1216 the smallest integer that is 183616 that is divisible by both numbers.
Least Common Multiple (LCM) of 1208 and 1216 is 183616.
LCM(1208,1216) = 183616
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 1216. First we will calculate the prime factors of 1208 and 1216.
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 1216
2 | 1216 |
2 | 608 |
2 | 304 |
2 | 152 |
2 | 76 |
2 | 38 |
19 | 19 |
1 |
Prime factors of 1216 are 2,19. Prime factorization of 1216 in exponential form is:
1216 = 26×191
Now multiplying the highest exponent prime factors to calculate the LCM of 1208 and 1216.
LCM(1208,1216) = 26×191×1511
LCM(1208,1216) = 183616
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 1216
List of positive integer factors of 1216 that divides 1216 without a remainder.
1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 608, 1216
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1208 and 1216, than apply into the LCM equation.
GCF(1208,1216) = 8
LCM(1208,1216) = ( 1208 × 1216) / 8
LCM(1208,1216) = 1468928 / 8
LCM(1208,1216) = 183616
(i) The LCM of 1216 and 1208 is associative
LCM of 1208 and 1216 = LCM of 1216 and 1208
1. What is the LCM of 1208 and 1216?
Answer: LCM of 1208 and 1216 is 183616.
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 1216?
Answer: Factors of 1216 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 608, 1216. There are 14 integers that are factors of 1216. The greatest factor of 1216 is 1216.
4. How to Find the LCM of 1208 and 1216?
Answer:
Least Common Multiple of 1208 and 1216 = 183616
Step 1: Find the prime factorization of 1208
1208 = 2 x 2 x 2 x 151
Step 2: Find the prime factorization of 1216
1216 = 2 x 2 x 2 x 2 x 2 x 2 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 183616 = 2 x 2 x 2 x 2 x 2 x 2 x 19 x 151
Step 4: Therefore, the least common multiple of 1208 and 1216 is 183616.