What is the Least Common Multiple of 36084 and 36096?

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 36084 and 36096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36084 and 36096, than apply into the LCM equation.

GCF(36084,36096) = 12
LCM(36084,36096) = ( 36084 × 36096) / 12
LCM(36084,36096) = 1302488064 / 12
LCM(36084,36096) = 108540672

Least Common Multiple (LCM) of 36084 and 36096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36084 and 36096. First we will calculate the prime factors of 36084 and 36096.

Prime Factorization of 36084

Prime Factorization of 36096

Now multiplying the highest exponent prime factors to calculate the LCM of 36084 and 36096.

LCM(36084,36096) = 2⁸ × 3¹ × 31¹ × 97¹ × 47¹
LCM(36084,36096) = 108540672