What is the Least Common Multiple of 39972 and 39980?

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 39980 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 39980, than apply into the LCM equation.

GCF(39972,39980) = 4
LCM(39972,39980) = ( 39972 × 39980) / 4
LCM(39972,39980) = 1598080560 / 4
LCM(39972,39980) = 399520140

Least Common Multiple (LCM) of 39972 and 39980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39972 and 39980. First we will calculate the prime factors of 39972 and 39980.

Prime Factorization of 39972

Prime Factorization of 39980

Now multiplying the highest exponent prime factors to calculate the LCM of 39972 and 39980.

LCM(39972,39980) = 2² × 3¹ × 3331¹ × 5¹ × 1999¹
LCM(39972,39980) = 399520140