What is the Least Common Multiple of 96105 and 96120?

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 96105 and 96120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96105 and 96120, than apply into the LCM equation.

GCF(96105,96120) = 15
LCM(96105,96120) = ( 96105 × 96120) / 15
LCM(96105,96120) = 9237612600 / 15
LCM(96105,96120) = 615840840

Least Common Multiple (LCM) of 96105 and 96120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 96105 and 96120. First we will calculate the prime factors of 96105 and 96120.

Prime Factorization of 96105

Prime Factorization of 96120

Now multiplying the highest exponent prime factors to calculate the LCM of 96105 and 96120.

LCM(96105,96120) = 3³ × 5¹ × 43¹ × 149¹ × 2³ × 89¹
LCM(96105,96120) = 615840840