What is the Least Common Multiple of 1500 and 1520?

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 1500 and 1520 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1500 and 1520, than apply into the LCM equation.

GCF(1500,1520) = 20
LCM(1500,1520) = ( 1500 × 1520) / 20
LCM(1500,1520) = 2280000 / 20
LCM(1500,1520) = 114000

Least Common Multiple (LCM) of 1500 and 1520 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1520. First we will calculate the prime factors of 1500 and 1520.

Prime Factorization of 1500

Prime Factorization of 1520

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1520.

LCM(1500,1520) = 2⁴ × 3¹ × 5³ × 19¹
LCM(1500,1520) = 114000