What is the Least Common Multiple of 39900 and 39915?

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 39900 and 39915 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39900 and 39915, than apply into the LCM equation.

GCF(39900,39915) = 15
LCM(39900,39915) = ( 39900 × 39915) / 15
LCM(39900,39915) = 1592608500 / 15
LCM(39900,39915) = 106173900

Least Common Multiple (LCM) of 39900 and 39915 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39900 and 39915. First we will calculate the prime factors of 39900 and 39915.

Prime Factorization of 39900

Prime Factorization of 39915

Now multiplying the highest exponent prime factors to calculate the LCM of 39900 and 39915.

LCM(39900,39915) = 2² × 3² × 5² × 7¹ × 19¹ × 887¹
LCM(39900,39915) = 106173900