Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 313 and 314 the smallest integer that is 98282 that is divisible by both numbers.
Least Common Multiple (LCM) of 313 and 314 is 98282.
LCM(313,314) = 98282
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 313 and 314. First we will calculate the prime factors of 313 and 314.
Prime Factorization of 313
313 | 313 |
1 |
Prime factors of 313 are 313. Prime factorization of 313 in exponential form is:
313 = 3131
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 313 and 314.
LCM(313,314) = 21×1571×3131
LCM(313,314) = 98282
Factors of 313
List of positive integer factors of 313 that divides 313 without a remainder.
1, 313
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 313 and 314, than apply into the LCM equation.
GCF(313,314) = 1
LCM(313,314) = ( 313 × 314) / 1
LCM(313,314) = 98282 / 1
LCM(313,314) = 98282
(i) The LCM of 314 and 313 is associative
LCM of 313 and 314 = LCM of 314 and 313
1. What is the LCM of 313 and 314?
Answer: LCM of 313 and 314 is 98282.
2. What are the Factors of 313?
Answer: Factors of 313 are 1, 313. There are 2 integers that are factors of 313. The greatest factor of 313 is 313.
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 313 and 314?
Answer:
Least Common Multiple of 313 and 314 = 98282
Step 1: Find the prime factorization of 313
313 = 313
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 = 98282 = 2 x 157 x 313
Step 4: Therefore, the least common multiple of 313 and 314 is 98282.