Least Common Multiple of 9981 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 9981 and 9984 the smallest integer that is 33216768 that is divisible by both numbers.

Least Common Multiple (LCM) of 9981 and 9984 is 33216768.

LCM(9981,9984) = 33216768

LCM of 9981 and 9984

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

LCM of:
and

Least Common Multiple of 9981 and 9984

LCM of 9981 and 9984 is 33216768

Least common multiple can be found by multiplying the highest exponent prime factors of 9981 and 9984. First we will calculate the prime factors of 9981 and 9984.

Prime Factorization of 9981


3 9981
3 3327
1109 1109
1

Prime factors of 9981 are 3,1109. Prime factorization of 9981 in exponential form is:

9981 = 32×11091

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 9981 and 9984.

LCM(9981,9984) = 28×32×131×11091
LCM(9981,9984) = 33216768

Factors of 9981

List of positive integer factors of 9981 that divides 9981 without a remainder.

1, 3, 9, 1109, 3327, 9981

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 9981 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 9981 and 9984, than apply into the LCM equation.

GCF(9981,9984) = 3
LCM(9981,9984) = ( 9981 × 9984) / 3
LCM(9981,9984) = 99650304 / 3
LCM(9981,9984) = 33216768

Properties of LCM 9981 and 9984

(i) The LCM of 9984 and 9981 is associative

LCM of 9981 and 9984 = LCM of 9984 and 9981

Related Least Common Multiples of 9981

Related Least Common Multiples of 9984

Frequently Asked Questions on LCM of 9981 and 9984

1. What is the LCM of 9981 and 9984?

Answer: LCM of 9981 and 9984 is 33216768.

2. What are the Factors of 9981?

Answer: Factors of 9981 are 1, 3, 9, 1109, 3327, 9981. There are 6 integers that are factors of 9981. The greatest factor of 9981 is 9981.

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 9981 and 9984?

Answer:

Least Common Multiple of 9981 and 9984 = 33216768

Step 1: Find the prime factorization of 9981

9981 = 3 x 3 x 1109

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 = 33216768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 1109

Step 4: Therefore, the least common multiple of 9981 and 9984 is 33216768.