Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9971 and 9978 the smallest integer that is 99490638 that is divisible by both numbers.
Least Common Multiple (LCM) of 9971 and 9978 is 99490638.
LCM(9971,9978) = 99490638
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 9971 and 9978. First we will calculate the prime factors of 9971 and 9978.
Prime Factorization of 9971
13 | 9971 |
13 | 767 |
59 | 59 |
1 |
Prime factors of 9971 are 13,59. Prime factorization of 9971 in exponential form is:
9971 = 132×591
Prime Factorization of 9978
2 | 9978 |
3 | 4989 |
1663 | 1663 |
1 |
Prime factors of 9978 are 2, 3,1663. Prime factorization of 9978 in exponential form is:
9978 = 21×31×16631
Now multiplying the highest exponent prime factors to calculate the LCM of 9971 and 9978.
LCM(9971,9978) = 21×31×132×591×16631
LCM(9971,9978) = 99490638
Factors of 9971
List of positive integer factors of 9971 that divides 9971 without a remainder.
1, 13, 59, 169, 767, 9971
Factors of 9978
List of positive integer factors of 9978 that divides 9978 without a remainder.
1, 2, 3, 6, 1663, 3326, 4989, 9978
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9971 and 9978, than apply into the LCM equation.
GCF(9971,9978) = 1
LCM(9971,9978) = ( 9971 × 9978) / 1
LCM(9971,9978) = 99490638 / 1
LCM(9971,9978) = 99490638
(i) The LCM of 9978 and 9971 is associative
LCM of 9971 and 9978 = LCM of 9978 and 9971
1. What is the LCM of 9971 and 9978?
Answer: LCM of 9971 and 9978 is 99490638.
2. What are the Factors of 9971?
Answer: Factors of 9971 are 1, 13, 59, 169, 767, 9971. There are 6 integers that are factors of 9971. The greatest factor of 9971 is 9971.
3. What are the Factors of 9978?
Answer: Factors of 9978 are 1, 2, 3, 6, 1663, 3326, 4989, 9978. There are 8 integers that are factors of 9978. The greatest factor of 9978 is 9978.
4. How to Find the LCM of 9971 and 9978?
Answer:
Least Common Multiple of 9971 and 9978 = 99490638
Step 1: Find the prime factorization of 9971
9971 = 13 x 13 x 59
Step 2: Find the prime factorization of 9978
9978 = 2 x 3 x 1663
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 99490638 = 2 x 3 x 13 x 13 x 59 x 1663
Step 4: Therefore, the least common multiple of 9971 and 9978 is 99490638.