What is the Least Common Multiple of 9732 and 9750?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 9732 and 9750 is 15814500.
LCM(9732,9750) = 15814500
Least Common Multiple of 9732 and 9750 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9732 and 9750, than apply into the LCM equation.
GCF(9732,9750) = 6
LCM(9732,9750) = ( 9732 × 9750) / 6
LCM(9732,9750) = 94887000 / 6
LCM(9732,9750) = 15814500
Least Common Multiple (LCM) of 9732 and 9750 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9732 and 9750. First we will calculate the prime factors of 9732 and 9750.
Prime Factorization of 9732
Prime factors of 9732 are 2, 3, 811. Prime factorization of 9732 in exponential form is:
9732 = 22 × 31 × 8111
Prime Factorization of 9750
Prime factors of 9750 are 2, 3, 5, 13. Prime factorization of 9750 in exponential form is:
9750 = 21 × 31 × 53 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 9732 and 9750.
LCM(9732,9750) = 22 × 31 × 8111 × 53 × 131
LCM(9732,9750) = 15814500
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