What is the Least Common Multiple of 76944 and 76960?

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 76944 and 76960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76944 and 76960, than apply into the LCM equation.

GCF(76944,76960) = 16
LCM(76944,76960) = ( 76944 × 76960) / 16
LCM(76944,76960) = 5921610240 / 16
LCM(76944,76960) = 370100640

Least Common Multiple (LCM) of 76944 and 76960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76944 and 76960. First we will calculate the prime factors of 76944 and 76960.

Prime Factorization of 76944

Prime Factorization of 76960

Now multiplying the highest exponent prime factors to calculate the LCM of 76944 and 76960.

LCM(76944,76960) = 2⁵ × 3¹ × 7¹ × 229¹ × 5¹ × 13¹ × 37¹
LCM(76944,76960) = 370100640