What is the Least Common Multiple of 67548 and 67560?

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 67548 and 67560 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67548 and 67560, than apply into the LCM equation.

GCF(67548,67560) = 12
LCM(67548,67560) = ( 67548 × 67560) / 12
LCM(67548,67560) = 4563542880 / 12
LCM(67548,67560) = 380295240

Least Common Multiple (LCM) of 67548 and 67560 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67548 and 67560. First we will calculate the prime factors of 67548 and 67560.

Prime Factorization of 67548

Prime Factorization of 67560

Now multiplying the highest exponent prime factors to calculate the LCM of 67548 and 67560.

LCM(67548,67560) = 2³ × 3¹ × 13¹ × 433¹ × 5¹ × 563¹
LCM(67548,67560) = 380295240