What is the Least Common Multiple of 67560 and 67575?

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 67560 and 67575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67560 and 67575, than apply into the LCM equation.

GCF(67560,67575) = 15
LCM(67560,67575) = ( 67560 × 67575) / 15
LCM(67560,67575) = 4565367000 / 15
LCM(67560,67575) = 304357800

Least Common Multiple (LCM) of 67560 and 67575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67560 and 67575. First we will calculate the prime factors of 67560 and 67575.

Prime Factorization of 67560

Prime Factorization of 67575

Now multiplying the highest exponent prime factors to calculate the LCM of 67560 and 67575.

LCM(67560,67575) = 2³ × 3¹ × 5² × 563¹ × 17¹ × 53¹
LCM(67560,67575) = 304357800