What is the Least Common Multiple of 1780 and 1800?

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 1780 and 1800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1780 and 1800, than apply into the LCM equation.

GCF(1780,1800) = 20
LCM(1780,1800) = ( 1780 × 1800) / 20
LCM(1780,1800) = 3204000 / 20
LCM(1780,1800) = 160200

Least Common Multiple (LCM) of 1780 and 1800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1780 and 1800. First we will calculate the prime factors of 1780 and 1800.

Prime Factorization of 1780

Prime Factorization of 1800

Now multiplying the highest exponent prime factors to calculate the LCM of 1780 and 1800.

LCM(1780,1800) = 2³ × 5² × 89¹ × 3²
LCM(1780,1800) = 160200