Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1311 and 1315 the smallest integer that is 1723965 that is divisible by both numbers.
Least Common Multiple (LCM) of 1311 and 1315 is 1723965.
LCM(1311,1315) = 1723965
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 1311 and 1315. First we will calculate the prime factors of 1311 and 1315.
Prime Factorization of 1311
3 | 1311 |
19 | 437 |
23 | 23 |
1 |
Prime factors of 1311 are 3, 19,23. Prime factorization of 1311 in exponential form is:
1311 = 31×191×231
Prime Factorization of 1315
5 | 1315 |
263 | 263 |
1 |
Prime factors of 1315 are 5,263. Prime factorization of 1315 in exponential form is:
1315 = 51×2631
Now multiplying the highest exponent prime factors to calculate the LCM of 1311 and 1315.
LCM(1311,1315) = 31×51×191×231×2631
LCM(1311,1315) = 1723965
Factors of 1311
List of positive integer factors of 1311 that divides 1311 without a remainder.
1, 3, 19, 23, 57, 69, 437, 1311
Factors of 1315
List of positive integer factors of 1315 that divides 1315 without a remainder.
1, 5, 263, 1315
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1311 and 1315, than apply into the LCM equation.
GCF(1311,1315) = 1
LCM(1311,1315) = ( 1311 × 1315) / 1
LCM(1311,1315) = 1723965 / 1
LCM(1311,1315) = 1723965
(i) The LCM of 1315 and 1311 is associative
LCM of 1311 and 1315 = LCM of 1315 and 1311
1. What is the LCM of 1311 and 1315?
Answer: LCM of 1311 and 1315 is 1723965.
2. What are the Factors of 1311?
Answer: Factors of 1311 are 1, 3, 19, 23, 57, 69, 437, 1311. There are 8 integers that are factors of 1311. The greatest factor of 1311 is 1311.
3. What are the Factors of 1315?
Answer: Factors of 1315 are 1, 5, 263, 1315. There are 4 integers that are factors of 1315. The greatest factor of 1315 is 1315.
4. How to Find the LCM of 1311 and 1315?
Answer:
Least Common Multiple of 1311 and 1315 = 1723965
Step 1: Find the prime factorization of 1311
1311 = 3 x 19 x 23
Step 2: Find the prime factorization of 1315
1315 = 5 x 263
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1723965 = 3 x 5 x 19 x 23 x 263
Step 4: Therefore, the least common multiple of 1311 and 1315 is 1723965.