Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9729 and 9736 the smallest integer that is 94721544 that is divisible by both numbers.
Least Common Multiple (LCM) of 9729 and 9736 is 94721544.
LCM(9729,9736) = 94721544
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 9729 and 9736. First we will calculate the prime factors of 9729 and 9736.
Prime Factorization of 9729
3 | 9729 |
3 | 3243 |
23 | 1081 |
47 | 47 |
1 |
Prime factors of 9729 are 3, 23,47. Prime factorization of 9729 in exponential form is:
9729 = 32×231×471
Prime Factorization of 9736
2 | 9736 |
2 | 4868 |
2 | 2434 |
1217 | 1217 |
1 |
Prime factors of 9736 are 2,1217. Prime factorization of 9736 in exponential form is:
9736 = 23×12171
Now multiplying the highest exponent prime factors to calculate the LCM of 9729 and 9736.
LCM(9729,9736) = 23×32×231×471×12171
LCM(9729,9736) = 94721544
Factors of 9729
List of positive integer factors of 9729 that divides 9729 without a remainder.
1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729
Factors of 9736
List of positive integer factors of 9736 that divides 9736 without a remainder.
1, 2, 4, 8, 1217, 2434, 4868, 9736
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9729 and 9736, than apply into the LCM equation.
GCF(9729,9736) = 1
LCM(9729,9736) = ( 9729 × 9736) / 1
LCM(9729,9736) = 94721544 / 1
LCM(9729,9736) = 94721544
(i) The LCM of 9736 and 9729 is associative
LCM of 9729 and 9736 = LCM of 9736 and 9729
1. What is the LCM of 9729 and 9736?
Answer: LCM of 9729 and 9736 is 94721544.
2. What are the Factors of 9729?
Answer: Factors of 9729 are 1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729. There are 12 integers that are factors of 9729. The greatest factor of 9729 is 9729.
3. What are the Factors of 9736?
Answer: Factors of 9736 are 1, 2, 4, 8, 1217, 2434, 4868, 9736. There are 8 integers that are factors of 9736. The greatest factor of 9736 is 9736.
4. How to Find the LCM of 9729 and 9736?
Answer:
Least Common Multiple of 9729 and 9736 = 94721544
Step 1: Find the prime factorization of 9729
9729 = 3 x 3 x 23 x 47
Step 2: Find the prime factorization of 9736
9736 = 2 x 2 x 2 x 1217
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 94721544 = 2 x 2 x 2 x 3 x 3 x 23 x 47 x 1217
Step 4: Therefore, the least common multiple of 9729 and 9736 is 94721544.