What is the Least Common Multiple of 1050 and 1065?

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 1050 and 1065 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1050 and 1065, than apply into the LCM equation.

GCF(1050,1065) = 15
LCM(1050,1065) = ( 1050 × 1065) / 15
LCM(1050,1065) = 1118250 / 15
LCM(1050,1065) = 74550

Least Common Multiple (LCM) of 1050 and 1065 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1050 and 1065. First we will calculate the prime factors of 1050 and 1065.

Prime Factorization of 1050

Prime Factorization of 1065

Now multiplying the highest exponent prime factors to calculate the LCM of 1050 and 1065.

LCM(1050,1065) = 2¹ × 3¹ × 5² × 7¹ × 71¹
LCM(1050,1065) = 74550