Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 319 and 320 the smallest integer that is 102080 that is divisible by both numbers.
Least Common Multiple (LCM) of 319 and 320 is 102080.
LCM(319,320) = 102080
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 319 and 320. First we will calculate the prime factors of 319 and 320.
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
Prime Factorization of 320
2 | 320 |
2 | 160 |
2 | 80 |
2 | 40 |
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 320 are 2,5. Prime factorization of 320 in exponential form is:
320 = 26×51
Now multiplying the highest exponent prime factors to calculate the LCM of 319 and 320.
LCM(319,320) = 26×51×111×291
LCM(319,320) = 102080
Factors of 319
List of positive integer factors of 319 that divides 319 without a remainder.
1, 11, 29, 319
Factors of 320
List of positive integer factors of 320 that divides 320 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 319 and 320, than apply into the LCM equation.
GCF(319,320) = 1
LCM(319,320) = ( 319 × 320) / 1
LCM(319,320) = 102080 / 1
LCM(319,320) = 102080
(i) The LCM of 320 and 319 is associative
LCM of 319 and 320 = LCM of 320 and 319
1. What is the LCM of 319 and 320?
Answer: LCM of 319 and 320 is 102080.
2. 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.
3. What are the Factors of 320?
Answer: Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. There are 14 integers that are factors of 320. The greatest factor of 320 is 320.
4. How to Find the LCM of 319 and 320?
Answer:
Least Common Multiple of 319 and 320 = 102080
Step 1: Find the prime factorization of 319
319 = 11 x 29
Step 2: Find the prime factorization of 320
320 = 2 x 2 x 2 x 2 x 2 x 2 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 102080 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 11 x 29
Step 4: Therefore, the least common multiple of 319 and 320 is 102080.