What is the Least Common Multiple of 1590 and 1610?

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 1590 and 1610 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1590 and 1610, than apply into the LCM equation.

GCF(1590,1610) = 10
LCM(1590,1610) = ( 1590 × 1610) / 10
LCM(1590,1610) = 2559900 / 10
LCM(1590,1610) = 255990

Least Common Multiple (LCM) of 1590 and 1610 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1590 and 1610. First we will calculate the prime factors of 1590 and 1610.

Prime Factorization of 1590

Prime Factorization of 1610

Now multiplying the highest exponent prime factors to calculate the LCM of 1590 and 1610.

LCM(1590,1610) = 2¹ × 3¹ × 5¹ × 53¹ × 7¹ × 23¹
LCM(1590,1610) = 255990