What is the Least Common Multiple of 19750 and 19770?

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 19750 and 19770 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19750 and 19770, than apply into the LCM equation.

GCF(19750,19770) = 10
LCM(19750,19770) = ( 19750 × 19770) / 10
LCM(19750,19770) = 390457500 / 10
LCM(19750,19770) = 39045750

Least Common Multiple (LCM) of 19750 and 19770 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19750 and 19770. First we will calculate the prime factors of 19750 and 19770.

Prime Factorization of 19750

Prime Factorization of 19770

Now multiplying the highest exponent prime factors to calculate the LCM of 19750 and 19770.

LCM(19750,19770) = 2¹ × 5³ × 79¹ × 3¹ × 659¹
LCM(19750,19770) = 39045750