What is the Least Common Multiple of 51675 and 51690?

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 51675 and 51690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51675 and 51690, than apply into the LCM equation.

GCF(51675,51690) = 15
LCM(51675,51690) = ( 51675 × 51690) / 15
LCM(51675,51690) = 2671080750 / 15
LCM(51675,51690) = 178072050

Least Common Multiple (LCM) of 51675 and 51690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51675 and 51690. First we will calculate the prime factors of 51675 and 51690.

Prime Factorization of 51675

Prime Factorization of 51690

Now multiplying the highest exponent prime factors to calculate the LCM of 51675 and 51690.

LCM(51675,51690) = 3¹ × 5² × 13¹ × 53¹ × 2¹ × 1723¹
LCM(51675,51690) = 178072050