What is the Least Common Multiple of 7968 and 7974?

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 7968 and 7974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7968 and 7974, than apply into the LCM equation.

GCF(7968,7974) = 6
LCM(7968,7974) = ( 7968 × 7974) / 6
LCM(7968,7974) = 63536832 / 6
LCM(7968,7974) = 10589472

Least Common Multiple (LCM) of 7968 and 7974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7968 and 7974. First we will calculate the prime factors of 7968 and 7974.

Prime Factorization of 7968

Prime Factorization of 7974

Now multiplying the highest exponent prime factors to calculate the LCM of 7968 and 7974.

LCM(7968,7974) = 2⁵ × 3² × 83¹ × 443¹
LCM(7968,7974) = 10589472