What is the Least Common Multiple of 21738 and 21758?

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 21738 and 21758 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21738 and 21758, than apply into the LCM equation.

GCF(21738,21758) = 2
LCM(21738,21758) = ( 21738 × 21758) / 2
LCM(21738,21758) = 472975404 / 2
LCM(21738,21758) = 236487702

Least Common Multiple (LCM) of 21738 and 21758 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21738 and 21758. First we will calculate the prime factors of 21738 and 21758.

Prime Factorization of 21738

Prime Factorization of 21758

Now multiplying the highest exponent prime factors to calculate the LCM of 21738 and 21758.

LCM(21738,21758) = 2¹ × 3¹ × 3623¹ × 11¹ × 23¹ × 43¹
LCM(21738,21758) = 236487702