What is the Least Common Multiple of 10410 and 10415?

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 10410 and 10415 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10410 and 10415, than apply into the LCM equation.

GCF(10410,10415) = 5
LCM(10410,10415) = ( 10410 × 10415) / 5
LCM(10410,10415) = 108420150 / 5
LCM(10410,10415) = 21684030

Least Common Multiple (LCM) of 10410 and 10415 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10410 and 10415. First we will calculate the prime factors of 10410 and 10415.

Prime Factorization of 10410

Prime Factorization of 10415

Now multiplying the highest exponent prime factors to calculate the LCM of 10410 and 10415.

LCM(10410,10415) = 2¹ × 3¹ × 5¹ × 347¹ × 2083¹
LCM(10410,10415) = 21684030