What is the Least Common Multiple of 39804 and 39824?

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 39804 and 39824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39804 and 39824, than apply into the LCM equation.

GCF(39804,39824) = 4
LCM(39804,39824) = ( 39804 × 39824) / 4
LCM(39804,39824) = 1585154496 / 4
LCM(39804,39824) = 396288624

Least Common Multiple (LCM) of 39804 and 39824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39804 and 39824. First we will calculate the prime factors of 39804 and 39824.

Prime Factorization of 39804

Prime Factorization of 39824

Now multiplying the highest exponent prime factors to calculate the LCM of 39804 and 39824.

LCM(39804,39824) = 2⁴ × 3¹ × 31¹ × 107¹ × 19¹ × 131¹
LCM(39804,39824) = 396288624