What is the Least Common Multiple of 30180 and 30192?

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 30180 and 30192 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30180 and 30192, than apply into the LCM equation.

GCF(30180,30192) = 12
LCM(30180,30192) = ( 30180 × 30192) / 12
LCM(30180,30192) = 911194560 / 12
LCM(30180,30192) = 75932880

Least Common Multiple (LCM) of 30180 and 30192 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30180 and 30192. First we will calculate the prime factors of 30180 and 30192.

Prime Factorization of 30180

Prime Factorization of 30192

Now multiplying the highest exponent prime factors to calculate the LCM of 30180 and 30192.

LCM(30180,30192) = 2⁴ × 3¹ × 5¹ × 503¹ × 17¹ × 37¹
LCM(30180,30192) = 75932880