What is the Least Common Multiple of 39840 and 39852?

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 39840 and 39852 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39840 and 39852, than apply into the LCM equation.

GCF(39840,39852) = 12
LCM(39840,39852) = ( 39840 × 39852) / 12
LCM(39840,39852) = 1587703680 / 12
LCM(39840,39852) = 132308640

Least Common Multiple (LCM) of 39840 and 39852 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39840 and 39852. First we will calculate the prime factors of 39840 and 39852.

Prime Factorization of 39840

Prime Factorization of 39852

Now multiplying the highest exponent prime factors to calculate the LCM of 39840 and 39852.

LCM(39840,39852) = 2⁵ × 3⁵ × 5¹ × 83¹ × 41¹
LCM(39840,39852) = 132308640