What is the Least Common Multiple of 20748 and 20762?

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 20748 and 20762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20748 and 20762, than apply into the LCM equation.

GCF(20748,20762) = 14
LCM(20748,20762) = ( 20748 × 20762) / 14
LCM(20748,20762) = 430769976 / 14
LCM(20748,20762) = 30769284

Least Common Multiple (LCM) of 20748 and 20762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20748 and 20762. First we will calculate the prime factors of 20748 and 20762.

Prime Factorization of 20748

Prime Factorization of 20762

Now multiplying the highest exponent prime factors to calculate the LCM of 20748 and 20762.

LCM(20748,20762) = 2² × 3¹ × 7¹ × 13¹ × 19¹ × 1483¹
LCM(20748,20762) = 30769284