What is the Least Common Multiple of 7725 and 7740?

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 7725 and 7740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7725 and 7740, than apply into the LCM equation.

GCF(7725,7740) = 15
LCM(7725,7740) = ( 7725 × 7740) / 15
LCM(7725,7740) = 59791500 / 15
LCM(7725,7740) = 3986100

Least Common Multiple (LCM) of 7725 and 7740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7725 and 7740. First we will calculate the prime factors of 7725 and 7740.

Prime Factorization of 7725

Prime Factorization of 7740

Now multiplying the highest exponent prime factors to calculate the LCM of 7725 and 7740.

LCM(7725,7740) = 3² × 5² × 103¹ × 2² × 43¹
LCM(7725,7740) = 3986100