What is the Least Common Multiple of 20805 and 20823?

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 20805 and 20823 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20805 and 20823, than apply into the LCM equation.

GCF(20805,20823) = 3
LCM(20805,20823) = ( 20805 × 20823) / 3
LCM(20805,20823) = 433222515 / 3
LCM(20805,20823) = 144407505

Least Common Multiple (LCM) of 20805 and 20823 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20805 and 20823. First we will calculate the prime factors of 20805 and 20823.

Prime Factorization of 20805

Prime Factorization of 20823

Now multiplying the highest exponent prime factors to calculate the LCM of 20805 and 20823.

LCM(20805,20823) = 3¹ × 5¹ × 19¹ × 73¹ × 11¹ × 631¹
LCM(20805,20823) = 144407505