What is the Least Common Multiple of 39996 and 40005?

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 39996 and 40005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39996 and 40005, than apply into the LCM equation.

GCF(39996,40005) = 9
LCM(39996,40005) = ( 39996 × 40005) / 9
LCM(39996,40005) = 1600039980 / 9
LCM(39996,40005) = 177782220

Least Common Multiple (LCM) of 39996 and 40005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39996 and 40005. First we will calculate the prime factors of 39996 and 40005.

Prime Factorization of 39996

Prime Factorization of 40005

Now multiplying the highest exponent prime factors to calculate the LCM of 39996 and 40005.

LCM(39996,40005) = 2² × 3² × 11¹ × 101¹ × 5¹ × 7¹ × 127¹
LCM(39996,40005) = 177782220