What is the Least Common Multiple of 42084 and 42096?

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 42084 and 42096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42084 and 42096, than apply into the LCM equation.

GCF(42084,42096) = 12
LCM(42084,42096) = ( 42084 × 42096) / 12
LCM(42084,42096) = 1771568064 / 12
LCM(42084,42096) = 147630672

Least Common Multiple (LCM) of 42084 and 42096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42084 and 42096. First we will calculate the prime factors of 42084 and 42096.

Prime Factorization of 42084

Prime Factorization of 42096

Now multiplying the highest exponent prime factors to calculate the LCM of 42084 and 42096.

LCM(42084,42096) = 2⁴ × 3² × 7¹ × 167¹ × 877¹
LCM(42084,42096) = 147630672