What is the Least Common Multiple of 39972 and 39984?

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 39972 and 39984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39972 and 39984, than apply into the LCM equation.

GCF(39972,39984) = 12
LCM(39972,39984) = ( 39972 × 39984) / 12
LCM(39972,39984) = 1598240448 / 12
LCM(39972,39984) = 133186704

Least Common Multiple (LCM) of 39972 and 39984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39972 and 39984. First we will calculate the prime factors of 39972 and 39984.

Prime Factorization of 39972

Prime Factorization of 39984

Now multiplying the highest exponent prime factors to calculate the LCM of 39972 and 39984.

LCM(39972,39984) = 2⁴ × 3¹ × 3331¹ × 7² × 17¹
LCM(39972,39984) = 133186704