Least Common Multiple of 1305 and 1313
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1305 and 1313 the smallest integer that is 1713465 that is divisible by both numbers.
Least Common Multiple (LCM) of 1305 and 1313 is 1713465.
LCM(1305,1313) = 1713465
LCM of 1305 and 1313
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1305 and 1313 by Prime method
- Least Common Multiple of 1305 and 1313 with GCF Formula
LCM of 1305 and 1313 is 1713465
Least common multiple can be found by multiplying the highest exponent prime factors of 1305 and 1313. First we will calculate the prime factors of 1305 and 1313.
Prime Factorization of 1305
| 3 | 1305 |
| 3 | 435 |
| 5 | 145 |
| 29 | 29 |
| 1 |
Prime factors of 1305 are 3, 5,29. Prime factorization of 1305 in exponential form is:
1305 = 32×51×291
Prime Factorization of 1313
| 13 | 1313 |
| 101 | 101 |
| 1 |
Prime factors of 1313 are 13,101. Prime factorization of 1313 in exponential form is:
1313 = 131×1011
Now multiplying the highest exponent prime factors to calculate the LCM of 1305 and 1313.
LCM(1305,1313) = 32×51×131×291×1011
LCM(1305,1313) = 1713465
Factors of 1305
List of positive integer factors of 1305 that divides 1305 without a remainder.
1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305
Factors of 1313
List of positive integer factors of 1313 that divides 1313 without a remainder.
1, 13, 101, 1313
Least Common Multiple of 1305 and 1313 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1305 and 1313, than apply into the LCM equation.
GCF(1305,1313) = 1
LCM(1305,1313) = ( 1305 × 1313) / 1
LCM(1305,1313) = 1713465 / 1
LCM(1305,1313) = 1713465
Properties of LCM 1305 and 1313
(i) The LCM of 1313 and 1305 is associative
LCM of 1305 and 1313 = LCM of 1313 and 1305
Related Least Common Multiples of 1305
Related Least Common Multiples of 1313
Frequently Asked Questions on LCM of 1305 and 1313
1. What is the LCM of 1305 and 1313?
Answer: LCM of 1305 and 1313 is 1713465.
2. What are the Factors of 1305?
Answer: Factors of 1305 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305. There are 12 integers that are factors of 1305. The greatest factor of 1305 is 1305.
3. What are the Factors of 1313?
Answer: Factors of 1313 are 1, 13, 101, 1313. There are 4 integers that are factors of 1313. The greatest factor of 1313 is 1313.
4. How to Find the LCM of 1305 and 1313?
Answer:
Least Common Multiple of 1305 and 1313 = 1713465
Step 1: Find the prime factorization of 1305
1305 = 3 x 3 x 5 x 29
Step 2: Find the prime factorization of 1313
1313 = 13 x 101
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1713465 = 3 x 3 x 5 x 13 x 29 x 101
Step 4: Therefore, the least common multiple of 1305 and 1313 is 1713465.