What is the Least Common Multiple of 1065 and 1075?

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 1065 and 1075 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1065 and 1075, than apply into the LCM equation.

GCF(1065,1075) = 5
LCM(1065,1075) = ( 1065 × 1075) / 5
LCM(1065,1075) = 1144875 / 5
LCM(1065,1075) = 228975

Least Common Multiple (LCM) of 1065 and 1075 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1065 and 1075. First we will calculate the prime factors of 1065 and 1075.

Prime Factorization of 1065

Prime Factorization of 1075

Now multiplying the highest exponent prime factors to calculate the LCM of 1065 and 1075.

LCM(1065,1075) = 3¹ × 5² × 71¹ × 43¹
LCM(1065,1075) = 228975