What is the Least Common Multiple of 99825 and 99840?

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 of 99825 and 99840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99825 and 99840, than apply into the LCM equation.

GCF(99825,99840) = 15
LCM(99825,99840) = ( 99825 × 99840) / 15
LCM(99825,99840) = 9966528000 / 15
LCM(99825,99840) = 664435200

Least Common Multiple (LCM) of 99825 and 99840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 99825 and 99840. First we will calculate the prime factors of 99825 and 99840.

Prime Factorization of 99825

Prime Factorization of 99840

Now multiplying the highest exponent prime factors to calculate the LCM of 99825 and 99840.

LCM(99825,99840) = 3¹ × 5² × 11³ × 2⁹ × 13¹
LCM(99825,99840) = 664435200