What is the Least Common Multiple of 7104 and 7112?

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 7104 and 7112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7104 and 7112, than apply into the LCM equation.

GCF(7104,7112) = 8
LCM(7104,7112) = ( 7104 × 7112) / 8
LCM(7104,7112) = 50523648 / 8
LCM(7104,7112) = 6315456

Least Common Multiple (LCM) of 7104 and 7112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7104 and 7112. First we will calculate the prime factors of 7104 and 7112.

Prime Factorization of 7104

Prime Factorization of 7112

Now multiplying the highest exponent prime factors to calculate the LCM of 7104 and 7112.

LCM(7104,7112) = 2⁶ × 3¹ × 37¹ × 7¹ × 127¹
LCM(7104,7112) = 6315456