Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9756 and 9759 the smallest integer that is 31736268 that is divisible by both numbers.
Least Common Multiple (LCM) of 9756 and 9759 is 31736268.
LCM(9756,9759) = 31736268
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 9756 and 9759. First we will calculate the prime factors of 9756 and 9759.
Prime Factorization of 9756
2 | 9756 |
2 | 4878 |
3 | 2439 |
3 | 813 |
271 | 271 |
1 |
Prime factors of 9756 are 2, 3,271. Prime factorization of 9756 in exponential form is:
9756 = 22×32×2711
Prime Factorization of 9759
3 | 9759 |
3253 | 3253 |
1 |
Prime factors of 9759 are 3,3253. Prime factorization of 9759 in exponential form is:
9759 = 31×32531
Now multiplying the highest exponent prime factors to calculate the LCM of 9756 and 9759.
LCM(9756,9759) = 22×32×2711×32531
LCM(9756,9759) = 31736268
Factors of 9756
List of positive integer factors of 9756 that divides 9756 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 36, 271, 542, 813, 1084, 1626, 2439, 3252, 4878, 9756
Factors of 9759
List of positive integer factors of 9759 that divides 9759 without a remainder.
1, 3, 3253, 9759
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9756 and 9759, than apply into the LCM equation.
GCF(9756,9759) = 3
LCM(9756,9759) = ( 9756 × 9759) / 3
LCM(9756,9759) = 95208804 / 3
LCM(9756,9759) = 31736268
(i) The LCM of 9759 and 9756 is associative
LCM of 9756 and 9759 = LCM of 9759 and 9756
1. What is the LCM of 9756 and 9759?
Answer: LCM of 9756 and 9759 is 31736268.
2. What are the Factors of 9756?
Answer: Factors of 9756 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 271, 542, 813, 1084, 1626, 2439, 3252, 4878, 9756. There are 18 integers that are factors of 9756. The greatest factor of 9756 is 9756.
3. What are the Factors of 9759?
Answer: Factors of 9759 are 1, 3, 3253, 9759. There are 4 integers that are factors of 9759. The greatest factor of 9759 is 9759.
4. How to Find the LCM of 9756 and 9759?
Answer:
Least Common Multiple of 9756 and 9759 = 31736268
Step 1: Find the prime factorization of 9756
9756 = 2 x 2 x 3 x 3 x 271
Step 2: Find the prime factorization of 9759
9759 = 3 x 3253
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 31736268 = 2 x 2 x 3 x 3 x 271 x 3253
Step 4: Therefore, the least common multiple of 9756 and 9759 is 31736268.