What is the Least Common Multiple of 39648 and 39663?

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 39648 and 39663 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39648 and 39663, than apply into the LCM equation.

GCF(39648,39663) = 3
LCM(39648,39663) = ( 39648 × 39663) / 3
LCM(39648,39663) = 1572558624 / 3
LCM(39648,39663) = 524186208

Least Common Multiple (LCM) of 39648 and 39663 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39648 and 39663. First we will calculate the prime factors of 39648 and 39663.

Prime Factorization of 39648

Prime Factorization of 39663

Now multiplying the highest exponent prime factors to calculate the LCM of 39648 and 39663.

LCM(39648,39663) = 2⁵ × 3³ × 7¹ × 59¹ × 13¹ × 113¹
LCM(39648,39663) = 524186208