What is the Least Common Multiple of 49104 and 49114?

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 49114 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 49114, than apply into the LCM equation.

GCF(49104,49114) = 2
LCM(49104,49114) = ( 49104 × 49114) / 2
LCM(49104,49114) = 2411693856 / 2
LCM(49104,49114) = 1205846928

Least Common Multiple (LCM) of 49104 and 49114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49104 and 49114. First we will calculate the prime factors of 49104 and 49114.

Prime Factorization of 49104

Prime Factorization of 49114

Now multiplying the highest exponent prime factors to calculate the LCM of 49104 and 49114.

LCM(49104,49114) = 2⁴ × 3² × 11¹ × 31¹ × 13¹ × 1889¹
LCM(49104,49114) = 1205846928