What is the Least Common Multiple of 67575 and 67584?

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 67575 and 67584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67575 and 67584, than apply into the LCM equation.

GCF(67575,67584) = 3
LCM(67575,67584) = ( 67575 × 67584) / 3
LCM(67575,67584) = 4566988800 / 3
LCM(67575,67584) = 1522329600

Least Common Multiple (LCM) of 67575 and 67584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67575 and 67584. First we will calculate the prime factors of 67575 and 67584.

Prime Factorization of 67575

Prime Factorization of 67584

Now multiplying the highest exponent prime factors to calculate the LCM of 67575 and 67584.

LCM(67575,67584) = 3¹ × 5² × 17¹ × 53¹ × 2¹¹ × 11¹
LCM(67575,67584) = 1522329600