Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1302 and 1309 the smallest integer that is 243474 that is divisible by both numbers.
Least Common Multiple (LCM) of 1302 and 1309 is 243474.
LCM(1302,1309) = 243474
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 1302 and 1309. First we will calculate the prime factors of 1302 and 1309.
Prime Factorization of 1302
2 | 1302 |
3 | 651 |
7 | 217 |
31 | 31 |
1 |
Prime factors of 1302 are 2, 3, 7,31. Prime factorization of 1302 in exponential form is:
1302 = 21×31×71×311
Prime Factorization of 1309
7 | 1309 |
11 | 187 |
17 | 17 |
1 |
Prime factors of 1309 are 7, 11,17. Prime factorization of 1309 in exponential form is:
1309 = 71×111×171
Now multiplying the highest exponent prime factors to calculate the LCM of 1302 and 1309.
LCM(1302,1309) = 21×31×71×111×171×311
LCM(1302,1309) = 243474
Factors of 1302
List of positive integer factors of 1302 that divides 1302 without a remainder.
1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302
Factors of 1309
List of positive integer factors of 1309 that divides 1309 without a remainder.
1, 7, 11, 17, 77, 119, 187, 1309
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1302 and 1309, than apply into the LCM equation.
GCF(1302,1309) = 7
LCM(1302,1309) = ( 1302 × 1309) / 7
LCM(1302,1309) = 1704318 / 7
LCM(1302,1309) = 243474
(i) The LCM of 1309 and 1302 is associative
LCM of 1302 and 1309 = LCM of 1309 and 1302
1. What is the LCM of 1302 and 1309?
Answer: LCM of 1302 and 1309 is 243474.
2. What are the Factors of 1302?
Answer: Factors of 1302 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302. There are 16 integers that are factors of 1302. The greatest factor of 1302 is 1302.
3. What are the Factors of 1309?
Answer: Factors of 1309 are 1, 7, 11, 17, 77, 119, 187, 1309. There are 8 integers that are factors of 1309. The greatest factor of 1309 is 1309.
4. How to Find the LCM of 1302 and 1309?
Answer:
Least Common Multiple of 1302 and 1309 = 243474
Step 1: Find the prime factorization of 1302
1302 = 2 x 3 x 7 x 31
Step 2: Find the prime factorization of 1309
1309 = 7 x 11 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 243474 = 2 x 3 x 7 x 11 x 17 x 31
Step 4: Therefore, the least common multiple of 1302 and 1309 is 243474.