Least Common Multiple of 9968 and 9976

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9968 and 9976 the smallest integer that is 12430096 that is divisible by both numbers.

Least Common Multiple (LCM) of 9968 and 9976 is 12430096.

LCM(9968,9976) = 12430096

LCM of 9968 and 9976

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

LCM of:
and

Least Common Multiple of 9968 and 9976

LCM of 9968 and 9976 is 12430096

Least common multiple can be found by multiplying the highest exponent prime factors of 9968 and 9976. First we will calculate the prime factors of 9968 and 9976.

Prime Factorization of 9968


2 9968
2 4984
2 2492
2 1246
7 623
89 89
1

Prime factors of 9968 are 2, 7,89. Prime factorization of 9968 in exponential form is:

9968 = 24×71×891

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

Now multiplying the highest exponent prime factors to calculate the LCM of 9968 and 9976.

LCM(9968,9976) = 24×71×291×431×891
LCM(9968,9976) = 12430096

Factors of 9968

List of positive integer factors of 9968 that divides 9968 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 89, 112, 178, 356, 623, 712, 1246, 1424, 2492, 4984, 9968

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

Least Common Multiple of 9968 and 9976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9968 and 9976, than apply into the LCM equation.

GCF(9968,9976) = 8
LCM(9968,9976) = ( 9968 × 9976) / 8
LCM(9968,9976) = 99440768 / 8
LCM(9968,9976) = 12430096

Properties of LCM 9968 and 9976

(i) The LCM of 9976 and 9968 is associative

LCM of 9968 and 9976 = LCM of 9976 and 9968

Related Least Common Multiples of 9968

Related Least Common Multiples of 9976

Frequently Asked Questions on LCM of 9968 and 9976

1. What is the LCM of 9968 and 9976?

Answer: LCM of 9968 and 9976 is 12430096.

2. What are the Factors of 9968?

Answer: Factors of 9968 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 89, 112, 178, 356, 623, 712, 1246, 1424, 2492, 4984, 9968. There are 20 integers that are factors of 9968. The greatest factor of 9968 is 9968.

3. 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.

4. How to Find the LCM of 9968 and 9976?

Answer:

Least Common Multiple of 9968 and 9976 = 12430096

Step 1: Find the prime factorization of 9968

9968 = 2 x 2 x 2 x 2 x 7 x 89

Step 2: Find the prime factorization of 9976

9976 = 2 x 2 x 2 x 29 x 43

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

LCM = 12430096 = 2 x 2 x 2 x 2 x 7 x 29 x 43 x 89

Step 4: Therefore, the least common multiple of 9968 and 9976 is 12430096.