What is the Least Common Multiple of 39825 and 39840?

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 39825 and 39840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39825 and 39840, than apply into the LCM equation.

GCF(39825,39840) = 15
LCM(39825,39840) = ( 39825 × 39840) / 15
LCM(39825,39840) = 1586628000 / 15
LCM(39825,39840) = 105775200

Least Common Multiple (LCM) of 39825 and 39840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39825 and 39840. First we will calculate the prime factors of 39825 and 39840.

Prime Factorization of 39825

Prime Factorization of 39840

Now multiplying the highest exponent prime factors to calculate the LCM of 39825 and 39840.

LCM(39825,39840) = 3³ × 5² × 59¹ × 2⁵ × 83¹
LCM(39825,39840) = 105775200