What is the Least Common Multiple of 49752 and 49760?

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 49752 and 49760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49752 and 49760, than apply into the LCM equation.

GCF(49752,49760) = 8
LCM(49752,49760) = ( 49752 × 49760) / 8
LCM(49752,49760) = 2475659520 / 8
LCM(49752,49760) = 309457440

Least Common Multiple (LCM) of 49752 and 49760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49752 and 49760. First we will calculate the prime factors of 49752 and 49760.

Prime Factorization of 49752

Prime Factorization of 49760

Now multiplying the highest exponent prime factors to calculate the LCM of 49752 and 49760.

LCM(49752,49760) = 2⁵ × 3² × 691¹ × 5¹ × 311¹
LCM(49752,49760) = 309457440