What is the Least Common Multiple of 67725 and 67740?

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 67725 and 67740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67725 and 67740, than apply into the LCM equation.

GCF(67725,67740) = 15
LCM(67725,67740) = ( 67725 × 67740) / 15
LCM(67725,67740) = 4587691500 / 15
LCM(67725,67740) = 305846100

Least Common Multiple (LCM) of 67725 and 67740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67725 and 67740. First we will calculate the prime factors of 67725 and 67740.

Prime Factorization of 67725

Prime Factorization of 67740

Now multiplying the highest exponent prime factors to calculate the LCM of 67725 and 67740.

LCM(67725,67740) = 3² × 5² × 7¹ × 43¹ × 2² × 1129¹
LCM(67725,67740) = 305846100