Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9972 and 9976 the smallest integer that is 24870168 that is divisible by both numbers.
Least Common Multiple (LCM) of 9972 and 9976 is 24870168.
LCM(9972,9976) = 24870168
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 9972 and 9976. First we will calculate the prime factors of 9972 and 9976.
Prime Factorization of 9972
2 | 9972 |
2 | 4986 |
3 | 2493 |
3 | 831 |
277 | 277 |
1 |
Prime factors of 9972 are 2, 3,277. Prime factorization of 9972 in exponential form is:
9972 = 22×32×2771
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
Now multiplying the highest exponent prime factors to calculate the LCM of 9972 and 9976.
LCM(9972,9976) = 23×32×291×431×2771
LCM(9972,9976) = 24870168
Factors of 9972
List of positive integer factors of 9972 that divides 9972 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9972 and 9976, than apply into the LCM equation.
GCF(9972,9976) = 4
LCM(9972,9976) = ( 9972 × 9976) / 4
LCM(9972,9976) = 99480672 / 4
LCM(9972,9976) = 24870168
(i) The LCM of 9976 and 9972 is associative
LCM of 9972 and 9976 = LCM of 9976 and 9972
1. What is the LCM of 9972 and 9976?
Answer: LCM of 9972 and 9976 is 24870168.
2. What are the Factors of 9972?
Answer: Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972. There are 18 integers that are factors of 9972. The greatest factor of 9972 is 9972.
3. 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.
4. How to Find the LCM of 9972 and 9976?
Answer:
Least Common Multiple of 9972 and 9976 = 24870168
Step 1: Find the prime factorization of 9972
9972 = 2 x 2 x 3 x 3 x 277
Step 2: Find the prime factorization of 9976
9976 = 2 x 2 x 2 x 29 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24870168 = 2 x 2 x 2 x 3 x 3 x 29 x 43 x 277
Step 4: Therefore, the least common multiple of 9972 and 9976 is 24870168.