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What is the Least Common Multiple of 9734 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 9734 and 9750 is 47453250.

LCM(9734,9750) = 47453250

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Least Common Multiple of 9734 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 9734 and 9750, than apply into the LCM equation.

GCF(9734,9750) = 2
LCM(9734,9750) = ( 9734 × 9750) / 2
LCM(9734,9750) = 94906500 / 2
LCM(9734,9750) = 47453250

Least Common Multiple (LCM) of 9734 and 9750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9734 and 9750. First we will calculate the prime factors of 9734 and 9750.

Prime Factorization of 9734

Prime factors of 9734 are 2, 31, 157. Prime factorization of 9734 in exponential form is:

9734 = 21 × 311 × 1571

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 9734 and 9750.

LCM(9734,9750) = 21 × 311 × 1571 × 31 × 53 × 131
LCM(9734,9750) = 47453250