What is the Least Common Multiple of 9972 and 9976?

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 9972 and 9976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9972 and 9976, than apply into the LCM equation.

GCF(9972,9976) = 4
LCM(9972,9976) = ( 9972 × 9976) / 4
LCM(9972,9976) = 99480672 / 4
LCM(9972,9976) = 24870168

Least Common Multiple (LCM) of 9972 and 9976 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9972 and 9976. First we will calculate the prime factors of 9972 and 9976.

Prime Factorization of 9972

Prime Factorization of 9976

Now multiplying the highest exponent prime factors to calculate the LCM of 9972 and 9976.

LCM(9972,9976) = 2³ × 3² × 277¹ × 29¹ × 43¹
LCM(9972,9976) = 24870168