Least Common Multiple of 9980 and 9984

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9980 and 9984 the smallest integer that is 24910080 that is divisible by both numbers.

Least Common Multiple (LCM) of 9980 and 9984 is 24910080.

LCM(9980,9984) = 24910080

LCM of 9980 and 9984

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

LCM of:
and

Least Common Multiple of 9980 and 9984

LCM of 9980 and 9984 is 24910080

Least common multiple can be found by multiplying the highest exponent prime factors of 9980 and 9984. First we will calculate the prime factors of 9980 and 9984.

Prime Factorization of 9980


2 9980
2 4990
5 2495
499 499
1

Prime factors of 9980 are 2, 5,499. Prime factorization of 9980 in exponential form is:

9980 = 22×51×4991

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

Now multiplying the highest exponent prime factors to calculate the LCM of 9980 and 9984.

LCM(9980,9984) = 28×31×51×131×4991
LCM(9980,9984) = 24910080

Factors of 9980

List of positive integer factors of 9980 that divides 9980 without a remainder.

1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990, 9980

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

Least Common Multiple of 9980 and 9984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9980 and 9984, than apply into the LCM equation.

GCF(9980,9984) = 4
LCM(9980,9984) = ( 9980 × 9984) / 4
LCM(9980,9984) = 99640320 / 4
LCM(9980,9984) = 24910080

Properties of LCM 9980 and 9984

(i) The LCM of 9984 and 9980 is associative

LCM of 9980 and 9984 = LCM of 9984 and 9980

Related Least Common Multiples of 9980

Related Least Common Multiples of 9984

Frequently Asked Questions on LCM of 9980 and 9984

1. What is the LCM of 9980 and 9984?

Answer: LCM of 9980 and 9984 is 24910080.

2. What are the Factors of 9980?

Answer: Factors of 9980 are 1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990, 9980. There are 12 integers that are factors of 9980. The greatest factor of 9980 is 9980.

3. 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.

4. How to Find the LCM of 9980 and 9984?

Answer:

Least Common Multiple of 9980 and 9984 = 24910080

Step 1: Find the prime factorization of 9980

9980 = 2 x 2 x 5 x 499

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 24910080 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 13 x 499

Step 4: Therefore, the least common multiple of 9980 and 9984 is 24910080.