Least Common Multiple of 9984 and 9988

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 9988 the smallest integer that is 24930048 that is divisible by both numbers.

Least Common Multiple (LCM) of 9984 and 9988 is 24930048.

LCM(9984,9988) = 24930048

LCM of 9984 and 9988

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

LCM of:
and

Least Common Multiple of 9984 and 9988

LCM of 9984 and 9988 is 24930048

Least common multiple can be found by multiplying the highest exponent prime factors of 9984 and 9988. First we will calculate the prime factors of 9984 and 9988.

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 9988


2 9988
2 4994
11 2497
227 227
1

Prime factors of 9988 are 2, 11,227. Prime factorization of 9988 in exponential form is:

9988 = 22×111×2271

Now multiplying the highest exponent prime factors to calculate the LCM of 9984 and 9988.

LCM(9984,9988) = 28×31×111×131×2271
LCM(9984,9988) = 24930048

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 9988

List of positive integer factors of 9988 that divides 9988 without a remainder.

1, 2, 4, 11, 22, 44, 227, 454, 908, 2497, 4994, 9988

Least Common Multiple of 9984 and 9988 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 9988, than apply into the LCM equation.

GCF(9984,9988) = 4
LCM(9984,9988) = ( 9984 × 9988) / 4
LCM(9984,9988) = 99720192 / 4
LCM(9984,9988) = 24930048

Properties of LCM 9984 and 9988

(i) The LCM of 9988 and 9984 is associative

LCM of 9984 and 9988 = LCM of 9988 and 9984

Related Least Common Multiples of 9984

Related Least Common Multiples of 9988

Frequently Asked Questions on LCM of 9984 and 9988

1. What is the LCM of 9984 and 9988?

Answer: LCM of 9984 and 9988 is 24930048.

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 9988?

Answer: Factors of 9988 are 1, 2, 4, 11, 22, 44, 227, 454, 908, 2497, 4994, 9988. There are 12 integers that are factors of 9988. The greatest factor of 9988 is 9988.

4. How to Find the LCM of 9984 and 9988?

Answer:

Least Common Multiple of 9984 and 9988 = 24930048

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 9988

9988 = 2 x 2 x 11 x 227

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

LCM = 24930048 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11 x 13 x 227

Step 4: Therefore, the least common multiple of 9984 and 9988 is 24930048.