Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 316 and 319 the smallest integer that is 100804 that is divisible by both numbers.
Least Common Multiple (LCM) of 316 and 319 is 100804.
LCM(316,319) = 100804
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 316 and 319. First we will calculate the prime factors of 316 and 319.
Prime Factorization of 316
2 | 316 |
2 | 158 |
79 | 79 |
1 |
Prime factors of 316 are 2,79. Prime factorization of 316 in exponential form is:
316 = 22×791
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 316 and 319.
LCM(316,319) = 22×111×291×791
LCM(316,319) = 100804
Factors of 316
List of positive integer factors of 316 that divides 316 without a remainder.
1, 2, 4, 79, 158, 316
Factors of 319
List of positive integer factors of 319 that divides 319 without a remainder.
1, 11, 29, 319
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 316 and 319, than apply into the LCM equation.
GCF(316,319) = 1
LCM(316,319) = ( 316 × 319) / 1
LCM(316,319) = 100804 / 1
LCM(316,319) = 100804
(i) The LCM of 319 and 316 is associative
LCM of 316 and 319 = LCM of 319 and 316
1. What is the LCM of 316 and 319?
Answer: LCM of 316 and 319 is 100804.
2. What are the Factors of 316?
Answer: Factors of 316 are 1, 2, 4, 79, 158, 316. There are 6 integers that are factors of 316. The greatest factor of 316 is 316.
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 316 and 319?
Answer:
Least Common Multiple of 316 and 319 = 100804
Step 1: Find the prime factorization of 316
316 = 2 x 2 x 79
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 = 100804 = 2 x 2 x 11 x 29 x 79
Step 4: Therefore, the least common multiple of 316 and 319 is 100804.