Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 308 and 312 the smallest integer that is 24024 that is divisible by both numbers.
Least Common Multiple (LCM) of 308 and 312 is 24024.
LCM(308,312) = 24024
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 308 and 312. First we will calculate the prime factors of 308 and 312.
Prime Factorization of 308
2 | 308 |
2 | 154 |
7 | 77 |
11 | 11 |
1 |
Prime factors of 308 are 2, 7,11. Prime factorization of 308 in exponential form is:
308 = 22×71×111
Prime Factorization of 312
2 | 312 |
2 | 156 |
2 | 78 |
3 | 39 |
13 | 13 |
1 |
Prime factors of 312 are 2, 3,13. Prime factorization of 312 in exponential form is:
312 = 23×31×131
Now multiplying the highest exponent prime factors to calculate the LCM of 308 and 312.
LCM(308,312) = 23×31×71×111×131
LCM(308,312) = 24024
Factors of 308
List of positive integer factors of 308 that divides 308 without a remainder.
1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
Factors of 312
List of positive integer factors of 312 that divides 312 without a remainder.
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 308 and 312, than apply into the LCM equation.
GCF(308,312) = 4
LCM(308,312) = ( 308 × 312) / 4
LCM(308,312) = 96096 / 4
LCM(308,312) = 24024
(i) The LCM of 312 and 308 is associative
LCM of 308 and 312 = LCM of 312 and 308
1. What is the LCM of 308 and 312?
Answer: LCM of 308 and 312 is 24024.
2. What are the Factors of 308?
Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.
3. What are the Factors of 312?
Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.
4. How to Find the LCM of 308 and 312?
Answer:
Least Common Multiple of 308 and 312 = 24024
Step 1: Find the prime factorization of 308
308 = 2 x 2 x 7 x 11
Step 2: Find the prime factorization of 312
312 = 2 x 2 x 2 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24024 = 2 x 2 x 2 x 3 x 7 x 11 x 13
Step 4: Therefore, the least common multiple of 308 and 312 is 24024.