What is the Least Common Multiple of 87105 and 87120?

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 87105 and 87120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 87105 and 87120, than apply into the LCM equation.

GCF(87105,87120) = 15
LCM(87105,87120) = ( 87105 × 87120) / 15
LCM(87105,87120) = 7588587600 / 15
LCM(87105,87120) = 505905840

Least Common Multiple (LCM) of 87105 and 87120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 87105 and 87120. First we will calculate the prime factors of 87105 and 87120.

Prime Factorization of 87105

Prime Factorization of 87120

Now multiplying the highest exponent prime factors to calculate the LCM of 87105 and 87120.

LCM(87105,87120) = 3² × 5¹ × 5807¹ × 2⁴ × 11²
LCM(87105,87120) = 505905840