What is the Least Common Multiple of 49728 and 49742?

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 49728 and 49742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49728 and 49742, than apply into the LCM equation.

GCF(49728,49742) = 14
LCM(49728,49742) = ( 49728 × 49742) / 14
LCM(49728,49742) = 2473570176 / 14
LCM(49728,49742) = 176683584

Least Common Multiple (LCM) of 49728 and 49742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49728 and 49742. First we will calculate the prime factors of 49728 and 49742.

Prime Factorization of 49728

Prime Factorization of 49742

Now multiplying the highest exponent prime factors to calculate the LCM of 49728 and 49742.

LCM(49728,49742) = 2⁶ × 3¹ × 7¹ × 37¹ × 11¹ × 17¹ × 19¹
LCM(49728,49742) = 176683584