What is the Least Common Multiple of 99105 and 99120?

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 99105 and 99120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99105 and 99120, than apply into the LCM equation.

GCF(99105,99120) = 15
LCM(99105,99120) = ( 99105 × 99120) / 15
LCM(99105,99120) = 9823287600 / 15
LCM(99105,99120) = 654885840

Least Common Multiple (LCM) of 99105 and 99120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 99105 and 99120. First we will calculate the prime factors of 99105 and 99120.

Prime Factorization of 99105

Prime Factorization of 99120

Now multiplying the highest exponent prime factors to calculate the LCM of 99105 and 99120.

LCM(99105,99120) = 3¹ × 5¹ × 6607¹ × 2⁴ × 7¹ × 59¹
LCM(99105,99120) = 654885840