Least Common Multiple of 314 and 319
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 314 and 319 the smallest integer that is 100166 that is divisible by both numbers.
Least Common Multiple (LCM) of 314 and 319 is 100166.
LCM(314,319) = 100166
LCM of 314 and 319
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 314 and 319 by Prime method
- Least Common Multiple of 314 and 319 with GCF Formula
LCM of 314 and 319 is 100166
Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 319. First we will calculate the prime factors of 314 and 319.
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
Prime Factorization of 319
| 11 | 319 |
| 29 | 29 |
| 1 |
Prime factors of 319 are 11,29. Prime factorization of 319 in exponential form is:
319 = 111×291
Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 319.
LCM(314,319) = 21×111×291×1571
LCM(314,319) = 100166
Factors of 314
List of positive integer factors of 314 that divides 314 without a remainder.
1, 2, 157, 314
Factors of 319
List of positive integer factors of 319 that divides 319 without a remainder.
1, 11, 29, 319
Least Common Multiple of 314 and 319 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 319, than apply into the LCM equation.
GCF(314,319) = 1
LCM(314,319) = ( 314 × 319) / 1
LCM(314,319) = 100166 / 1
LCM(314,319) = 100166
Properties of LCM 314 and 319
(i) The LCM of 319 and 314 is associative
LCM of 314 and 319 = LCM of 319 and 314
Related Least Common Multiples of 314
Related Least Common Multiples of 319
Frequently Asked Questions on LCM of 314 and 319
1. What is the LCM of 314 and 319?
Answer: LCM of 314 and 319 is 100166.
2. 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.
3. What are the Factors of 319?
Answer: Factors of 319 are 1, 11, 29, 319. There are 4 integers that are factors of 319. The greatest factor of 319 is 319.
4. How to Find the LCM of 314 and 319?
Answer:
Least Common Multiple of 314 and 319 = 100166
Step 1: Find the prime factorization of 314
314 = 2 x 157
Step 2: Find the prime factorization of 319
319 = 11 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100166 = 2 x 11 x 29 x 157
Step 4: Therefore, the least common multiple of 314 and 319 is 100166.