What is the Least Common Multiple of 820 and 825?

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 820 and 825 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 820 and 825, than apply into the LCM equation.

GCF(820,825) = 5
LCM(820,825) = ( 820 × 825) / 5
LCM(820,825) = 676500 / 5
LCM(820,825) = 135300

Least Common Multiple (LCM) of 820 and 825 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 820 and 825. First we will calculate the prime factors of 820 and 825.

Prime Factorization of 820

Prime Factorization of 825

Now multiplying the highest exponent prime factors to calculate the LCM of 820 and 825.

LCM(820,825) = 2² × 5² × 41¹ × 3¹ × 11¹
LCM(820,825) = 135300