Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 312 and 314 the smallest integer that is 48984 that is divisible by both numbers.
Least Common Multiple (LCM) of 312 and 314 is 48984.
LCM(312,314) = 48984
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 312 and 314. First we will calculate the prime factors of 312 and 314.
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
Prime Factorization of 314
2 | 314 |
157 | 157 |
1 |
Prime factors of 314 are 2,157. Prime factorization of 314 in exponential form is:
314 = 21×1571
Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 314.
LCM(312,314) = 23×31×131×1571
LCM(312,314) = 48984
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
Factors of 314
List of positive integer factors of 314 that divides 314 without a remainder.
1, 2, 157, 314
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 314, than apply into the LCM equation.
GCF(312,314) = 2
LCM(312,314) = ( 312 × 314) / 2
LCM(312,314) = 97968 / 2
LCM(312,314) = 48984
(i) The LCM of 314 and 312 is associative
LCM of 312 and 314 = LCM of 314 and 312
1. What is the LCM of 312 and 314?
Answer: LCM of 312 and 314 is 48984.
2. 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.
3. What are the Factors of 314?
Answer: Factors of 314 are 1, 2, 157, 314. There are 4 integers that are factors of 314. The greatest factor of 314 is 314.
4. How to Find the LCM of 312 and 314?
Answer:
Least Common Multiple of 312 and 314 = 48984
Step 1: Find the prime factorization of 312
312 = 2 x 2 x 2 x 3 x 13
Step 2: Find the prime factorization of 314
314 = 2 x 157
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 48984 = 2 x 2 x 2 x 3 x 13 x 157
Step 4: Therefore, the least common multiple of 312 and 314 is 48984.