What is the Least Common Multiple of 49104 and 49119?

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 49104 and 49119 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49104 and 49119, than apply into the LCM equation.

GCF(49104,49119) = 3
LCM(49104,49119) = ( 49104 × 49119) / 3
LCM(49104,49119) = 2411939376 / 3
LCM(49104,49119) = 803979792

Least Common Multiple (LCM) of 49104 and 49119 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49104 and 49119. First we will calculate the prime factors of 49104 and 49119.

Prime Factorization of 49104

Prime Factorization of 49119

Now multiplying the highest exponent prime factors to calculate the LCM of 49104 and 49119.

LCM(49104,49119) = 2⁴ × 3² × 11¹ × 31¹ × 7¹ × 2339¹
LCM(49104,49119) = 803979792