What is the Least Common Multiple of 36192 and 36204?

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 36192 and 36204 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36192 and 36204, than apply into the LCM equation.

GCF(36192,36204) = 12
LCM(36192,36204) = ( 36192 × 36204) / 12
LCM(36192,36204) = 1310295168 / 12
LCM(36192,36204) = 109191264

Least Common Multiple (LCM) of 36192 and 36204 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36192 and 36204. First we will calculate the prime factors of 36192 and 36204.

Prime Factorization of 36192

Prime Factorization of 36204

Now multiplying the highest exponent prime factors to calculate the LCM of 36192 and 36204.

LCM(36192,36204) = 2⁵ × 3¹ × 13¹ × 29¹ × 7¹ × 431¹
LCM(36192,36204) = 109191264