Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 12305 and 12313 the smallest integer that is 151511465 that is divisible by both numbers.
Least Common Multiple (LCM) of 12305 and 12313 is 151511465.
LCM(12305,12313) = 151511465
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 12305 and 12313. First we will calculate the prime factors of 12305 and 12313.
Prime Factorization of 12305
5 | 12305 |
23 | 2461 |
107 | 107 |
1 |
Prime factors of 12305 are 5, 23,107. Prime factorization of 12305 in exponential form is:
12305 = 51×231×1071
Prime Factorization of 12313
7 | 12313 |
1759 | 1759 |
1 |
Prime factors of 12313 are 7,1759. Prime factorization of 12313 in exponential form is:
12313 = 71×17591
Now multiplying the highest exponent prime factors to calculate the LCM of 12305 and 12313.
LCM(12305,12313) = 51×71×231×1071×17591
LCM(12305,12313) = 151511465
Factors of 12305
List of positive integer factors of 12305 that divides 12305 without a remainder.
1, 5, 23, 107, 115, 535, 2461, 12305
Factors of 12313
List of positive integer factors of 12313 that divides 12313 without a remainder.
1, 7, 1759, 12313
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12305 and 12313, than apply into the LCM equation.
GCF(12305,12313) = 1
LCM(12305,12313) = ( 12305 × 12313) / 1
LCM(12305,12313) = 151511465 / 1
LCM(12305,12313) = 151511465
(i) The LCM of 12313 and 12305 is associative
LCM of 12305 and 12313 = LCM of 12313 and 12305
1. What is the LCM of 12305 and 12313?
Answer: LCM of 12305 and 12313 is 151511465.
2. What are the Factors of 12305?
Answer: Factors of 12305 are 1, 5, 23, 107, 115, 535, 2461, 12305. There are 8 integers that are factors of 12305. The greatest factor of 12305 is 12305.
3. What are the Factors of 12313?
Answer: Factors of 12313 are 1, 7, 1759, 12313. There are 4 integers that are factors of 12313. The greatest factor of 12313 is 12313.
4. How to Find the LCM of 12305 and 12313?
Answer:
Least Common Multiple of 12305 and 12313 = 151511465
Step 1: Find the prime factorization of 12305
12305 = 5 x 23 x 107
Step 2: Find the prime factorization of 12313
12313 = 7 x 1759
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 151511465 = 5 x 7 x 23 x 107 x 1759
Step 4: Therefore, the least common multiple of 12305 and 12313 is 151511465.