Least Common Multiple of 9984 and 9992

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9984 and 9992 the smallest integer that is 12470016 that is divisible by both numbers.

Least Common Multiple (LCM) of 9984 and 9992 is 12470016.

LCM(9984,9992) = 12470016

LCM of 9984 and 9992

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

LCM of:
and

Least Common Multiple of 9984 and 9992

LCM of 9984 and 9992 is 12470016

Least common multiple can be found by multiplying the highest exponent prime factors of 9984 and 9992. First we will calculate the prime factors of 9984 and 9992.

Prime Factorization of 9984


2 9984
2 4992
2 2496
2 1248
2 624
2 312
2 156
2 78
3 39
13 13
1

Prime factors of 9984 are 2, 3,13. Prime factorization of 9984 in exponential form is:

9984 = 28×31×131

Prime Factorization of 9992


2 9992
2 4996
2 2498
1249 1249
1

Prime factors of 9992 are 2,1249. Prime factorization of 9992 in exponential form is:

9992 = 23×12491

Now multiplying the highest exponent prime factors to calculate the LCM of 9984 and 9992.

LCM(9984,9992) = 28×31×131×12491
LCM(9984,9992) = 12470016

Factors of 9984

List of positive integer factors of 9984 that divides 9984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984

Factors of 9992

List of positive integer factors of 9992 that divides 9992 without a remainder.

1, 2, 4, 8, 1249, 2498, 4996, 9992

Least Common Multiple of 9984 and 9992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9984 and 9992, than apply into the LCM equation.

GCF(9984,9992) = 8
LCM(9984,9992) = ( 9984 × 9992) / 8
LCM(9984,9992) = 99760128 / 8
LCM(9984,9992) = 12470016

Properties of LCM 9984 and 9992

(i) The LCM of 9992 and 9984 is associative

LCM of 9984 and 9992 = LCM of 9992 and 9984

Related Least Common Multiples of 9984

Related Least Common Multiples of 9992

Frequently Asked Questions on LCM of 9984 and 9992

1. What is the LCM of 9984 and 9992?

Answer: LCM of 9984 and 9992 is 12470016.

2. What are the Factors of 9984?

Answer: Factors of 9984 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984. There are 36 integers that are factors of 9984. The greatest factor of 9984 is 9984.

3. What are the Factors of 9992?

Answer: Factors of 9992 are 1, 2, 4, 8, 1249, 2498, 4996, 9992. There are 8 integers that are factors of 9992. The greatest factor of 9992 is 9992.

4. How to Find the LCM of 9984 and 9992?

Answer:

Least Common Multiple of 9984 and 9992 = 12470016

Step 1: Find the prime factorization of 9984

9984 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13

Step 2: Find the prime factorization of 9992

9992 = 2 x 2 x 2 x 1249

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

LCM = 12470016 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 1249

Step 4: Therefore, the least common multiple of 9984 and 9992 is 12470016.