What is the Least Common Multiple of 42084 and 42100?

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 42100 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 42100, than apply into the LCM equation.

GCF(42084,42100) = 4
LCM(42084,42100) = ( 42084 × 42100) / 4
LCM(42084,42100) = 1771736400 / 4
LCM(42084,42100) = 442934100

Least Common Multiple (LCM) of 42084 and 42100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42084 and 42100. First we will calculate the prime factors of 42084 and 42100.

Prime Factorization of 42084

Prime Factorization of 42100

Now multiplying the highest exponent prime factors to calculate the LCM of 42084 and 42100.

LCM(42084,42100) = 2² × 3² × 7¹ × 167¹ × 5² × 421¹
LCM(42084,42100) = 442934100