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 9974 the smallest integer that is 49730364 that is divisible by both numbers.
Least Common Multiple (LCM) of 9972 and 9974 is 49730364.
LCM(9972,9974) = 49730364
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 9974. First we will calculate the prime factors of 9972 and 9974.
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 9974
2 | 9974 |
4987 | 4987 |
1 |
Prime factors of 9974 are 2,4987. Prime factorization of 9974 in exponential form is:
9974 = 21×49871
Now multiplying the highest exponent prime factors to calculate the LCM of 9972 and 9974.
LCM(9972,9974) = 22×32×2771×49871
LCM(9972,9974) = 49730364
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 9974
List of positive integer factors of 9974 that divides 9974 without a remainder.
1, 2, 4987, 9974
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9972 and 9974, than apply into the LCM equation.
GCF(9972,9974) = 2
LCM(9972,9974) = ( 9972 × 9974) / 2
LCM(9972,9974) = 99460728 / 2
LCM(9972,9974) = 49730364
(i) The LCM of 9974 and 9972 is associative
LCM of 9972 and 9974 = LCM of 9974 and 9972
1. What is the LCM of 9972 and 9974?
Answer: LCM of 9972 and 9974 is 49730364.
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 9974?
Answer: Factors of 9974 are 1, 2, 4987, 9974. There are 4 integers that are factors of 9974. The greatest factor of 9974 is 9974.
4. How to Find the LCM of 9972 and 9974?
Answer:
Least Common Multiple of 9972 and 9974 = 49730364
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 9974
9974 = 2 x 4987
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 49730364 = 2 x 2 x 3 x 3 x 277 x 4987
Step 4: Therefore, the least common multiple of 9972 and 9974 is 49730364.