What is the Least Common Multiple of 7008 and 7024?

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 7008 and 7024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7008 and 7024, than apply into the LCM equation.

GCF(7008,7024) = 16
LCM(7008,7024) = ( 7008 × 7024) / 16
LCM(7008,7024) = 49224192 / 16
LCM(7008,7024) = 3076512

Least Common Multiple (LCM) of 7008 and 7024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7008 and 7024. First we will calculate the prime factors of 7008 and 7024.

Prime Factorization of 7008

Prime Factorization of 7024

Now multiplying the highest exponent prime factors to calculate the LCM of 7008 and 7024.

LCM(7008,7024) = 2⁵ × 3¹ × 73¹ × 439¹
LCM(7008,7024) = 3076512