What is the Least Common Multiple of 15105 and 15120?

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 15105 and 15120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15105 and 15120, than apply into the LCM equation.

GCF(15105,15120) = 15
LCM(15105,15120) = ( 15105 × 15120) / 15
LCM(15105,15120) = 228387600 / 15
LCM(15105,15120) = 15225840

Least Common Multiple (LCM) of 15105 and 15120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15105 and 15120. First we will calculate the prime factors of 15105 and 15120.

Prime Factorization of 15105

Prime Factorization of 15120

Now multiplying the highest exponent prime factors to calculate the LCM of 15105 and 15120.

LCM(15105,15120) = 3³ × 5¹ × 19¹ × 53¹ × 2⁴ × 7¹
LCM(15105,15120) = 15225840