Least Common Multiple of 9976 and 9982

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9976 and 9982 the smallest integer that is 49790216 that is divisible by both numbers.

Least Common Multiple (LCM) of 9976 and 9982 is 49790216.

LCM(9976,9982) = 49790216

LCM of 9976 and 9982

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 9976 and 9982

LCM of 9976 and 9982 is 49790216

Least common multiple can be found by multiplying the highest exponent prime factors of 9976 and 9982. First we will calculate the prime factors of 9976 and 9982.

Prime Factorization of 9976


2 9976
2 4988
2 2494
29 1247
43 43
1

Prime factors of 9976 are 2, 29,43. Prime factorization of 9976 in exponential form is:

9976 = 23×291×431

Prime Factorization of 9982


2 9982
7 4991
23 713
31 31
1

Prime factors of 9982 are 2, 7, 23,31. Prime factorization of 9982 in exponential form is:

9982 = 21×71×231×311

Now multiplying the highest exponent prime factors to calculate the LCM of 9976 and 9982.

LCM(9976,9982) = 23×71×231×291×311×431
LCM(9976,9982) = 49790216

Factors of 9976

List of positive integer factors of 9976 that divides 9976 without a remainder.

1, 2, 4, 8, 29, 43, 58, 86, 116, 172, 232, 344, 1247, 2494, 4988, 9976

Factors of 9982

List of positive integer factors of 9982 that divides 9982 without a remainder.

1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982

Least Common Multiple of 9976 and 9982 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9976 and 9982, than apply into the LCM equation.

GCF(9976,9982) = 2
LCM(9976,9982) = ( 9976 × 9982) / 2
LCM(9976,9982) = 99580432 / 2
LCM(9976,9982) = 49790216

Properties of LCM 9976 and 9982

(i) The LCM of 9982 and 9976 is associative

LCM of 9976 and 9982 = LCM of 9982 and 9976

Related Least Common Multiples of 9976

Related Least Common Multiples of 9982

Frequently Asked Questions on LCM of 9976 and 9982

1. What is the LCM of 9976 and 9982?

Answer: LCM of 9976 and 9982 is 49790216.

2. What are the Factors of 9976?

Answer: Factors of 9976 are 1, 2, 4, 8, 29, 43, 58, 86, 116, 172, 232, 344, 1247, 2494, 4988, 9976. There are 16 integers that are factors of 9976. The greatest factor of 9976 is 9976.

3. What are the Factors of 9982?

Answer: Factors of 9982 are 1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982. There are 16 integers that are factors of 9982. The greatest factor of 9982 is 9982.

4. How to Find the LCM of 9976 and 9982?

Answer:

Least Common Multiple of 9976 and 9982 = 49790216

Step 1: Find the prime factorization of 9976

9976 = 2 x 2 x 2 x 29 x 43

Step 2: Find the prime factorization of 9982

9982 = 2 x 7 x 23 x 31

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 49790216 = 2 x 2 x 2 x 7 x 23 x 29 x 31 x 43

Step 4: Therefore, the least common multiple of 9976 and 9982 is 49790216.