What is the Least Common Multiple of 49714 and 49728?

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 49714 and 49728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49714 and 49728, than apply into the LCM equation.

GCF(49714,49728) = 14
LCM(49714,49728) = ( 49714 × 49728) / 14
LCM(49714,49728) = 2472177792 / 14
LCM(49714,49728) = 176584128

Least Common Multiple (LCM) of 49714 and 49728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49714 and 49728. First we will calculate the prime factors of 49714 and 49728.

Prime Factorization of 49714

Prime Factorization of 49728

Now multiplying the highest exponent prime factors to calculate the LCM of 49714 and 49728.

LCM(49714,49728) = 2⁶ × 7¹ × 53¹ × 67¹ × 3¹ × 37¹
LCM(49714,49728) = 176584128