Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 307 and 314 the smallest integer that is 96398 that is divisible by both numbers.
Least Common Multiple (LCM) of 307 and 314 is 96398.
LCM(307,314) = 96398
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 307 and 314. First we will calculate the prime factors of 307 and 314.
Prime Factorization of 307
307 | 307 |
1 |
Prime factors of 307 are 307. Prime factorization of 307 in exponential form is:
307 = 3071
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 307 and 314.
LCM(307,314) = 21×1571×3071
LCM(307,314) = 96398
Factors of 307
List of positive integer factors of 307 that divides 307 without a remainder.
1, 307
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 307 and 314, than apply into the LCM equation.
GCF(307,314) = 1
LCM(307,314) = ( 307 × 314) / 1
LCM(307,314) = 96398 / 1
LCM(307,314) = 96398
(i) The LCM of 314 and 307 is associative
LCM of 307 and 314 = LCM of 314 and 307
1. What is the LCM of 307 and 314?
Answer: LCM of 307 and 314 is 96398.
2. What are the Factors of 307?
Answer: Factors of 307 are 1, 307. There are 2 integers that are factors of 307. The greatest factor of 307 is 307.
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 307 and 314?
Answer:
Least Common Multiple of 307 and 314 = 96398
Step 1: Find the prime factorization of 307
307 = 307
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 = 96398 = 2 x 157 x 307
Step 4: Therefore, the least common multiple of 307 and 314 is 96398.