What is the Least Common Multiple of 20805 and 20824?

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 20824 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 20824, than apply into the LCM equation.

GCF(20805,20824) = 19
LCM(20805,20824) = ( 20805 × 20824) / 19
LCM(20805,20824) = 433243320 / 19
LCM(20805,20824) = 22802280

Least Common Multiple (LCM) of 20805 and 20824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20805 and 20824. First we will calculate the prime factors of 20805 and 20824.

Prime Factorization of 20805

Prime Factorization of 20824

Now multiplying the highest exponent prime factors to calculate the LCM of 20805 and 20824.

LCM(20805,20824) = 3¹ × 5¹ × 19¹ × 73¹ × 2³ × 137¹
LCM(20805,20824) = 22802280