What is the Least Common Multiple of 3975 and 3984?

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 3975 and 3984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3975 and 3984, than apply into the LCM equation.

GCF(3975,3984) = 3
LCM(3975,3984) = ( 3975 × 3984) / 3
LCM(3975,3984) = 15836400 / 3
LCM(3975,3984) = 5278800

Least Common Multiple (LCM) of 3975 and 3984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3975 and 3984. First we will calculate the prime factors of 3975 and 3984.

Prime Factorization of 3975

Prime Factorization of 3984

Now multiplying the highest exponent prime factors to calculate the LCM of 3975 and 3984.

LCM(3975,3984) = 3¹ × 5² × 53¹ × 2⁴ × 83¹
LCM(3975,3984) = 5278800