Least Common Multiple of 9976 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 9976 and 9984 the smallest integer that is 12450048 that is divisible by both numbers.

Least Common Multiple (LCM) of 9976 and 9984 is 12450048.

LCM(9976,9984) = 12450048

LCM of 9976 and 9984

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

LCM of:
and

Least Common Multiple of 9976 and 9984

LCM of 9976 and 9984 is 12450048

Least common multiple can be found by multiplying the highest exponent prime factors of 9976 and 9984. First we will calculate the prime factors of 9976 and 9984.

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

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 9976 and 9984.

LCM(9976,9984) = 28×31×131×291×431
LCM(9976,9984) = 12450048

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

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 9976 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 9976 and 9984, than apply into the LCM equation.

GCF(9976,9984) = 8
LCM(9976,9984) = ( 9976 × 9984) / 8
LCM(9976,9984) = 99600384 / 8
LCM(9976,9984) = 12450048

Properties of LCM 9976 and 9984

(i) The LCM of 9984 and 9976 is associative

LCM of 9976 and 9984 = LCM of 9984 and 9976

Related Least Common Multiples of 9976

Related Least Common Multiples of 9984

Frequently Asked Questions on LCM of 9976 and 9984

1. What is the LCM of 9976 and 9984?

Answer: LCM of 9976 and 9984 is 12450048.

2. 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.

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 9976 and 9984?

Answer:

Least Common Multiple of 9976 and 9984 = 12450048

Step 1: Find the prime factorization of 9976

9976 = 2 x 2 x 2 x 29 x 43

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 = 12450048 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 29 x 43

Step 4: Therefore, the least common multiple of 9976 and 9984 is 12450048.