What is the Least Common Multiple of 7742 and 7760?

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 7742 and 7760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7742 and 7760, than apply into the LCM equation.

GCF(7742,7760) = 2
LCM(7742,7760) = ( 7742 × 7760) / 2
LCM(7742,7760) = 60077920 / 2
LCM(7742,7760) = 30038960

Least Common Multiple (LCM) of 7742 and 7760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7742 and 7760. First we will calculate the prime factors of 7742 and 7760.

Prime Factorization of 7742

Prime Factorization of 7760

Now multiplying the highest exponent prime factors to calculate the LCM of 7742 and 7760.

LCM(7742,7760) = 2⁴ × 7² × 79¹ × 5¹ × 97¹
LCM(7742,7760) = 30038960