What is the Least Common Multiple of 825 and 830?

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 825 and 830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 825 and 830, than apply into the LCM equation.

GCF(825,830) = 5
LCM(825,830) = ( 825 × 830) / 5
LCM(825,830) = 684750 / 5
LCM(825,830) = 136950

Least Common Multiple (LCM) of 825 and 830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 825 and 830. First we will calculate the prime factors of 825 and 830.

Prime Factorization of 825

Prime Factorization of 830

Now multiplying the highest exponent prime factors to calculate the LCM of 825 and 830.

LCM(825,830) = 3¹ × 5² × 11¹ × 2¹ × 83¹
LCM(825,830) = 136950