What is the Least Common Multiple of 9825 and 9834?

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 9825 and 9834 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9825 and 9834, than apply into the LCM equation.

GCF(9825,9834) = 3
LCM(9825,9834) = ( 9825 × 9834) / 3
LCM(9825,9834) = 96619050 / 3
LCM(9825,9834) = 32206350

Least Common Multiple (LCM) of 9825 and 9834 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9825 and 9834. First we will calculate the prime factors of 9825 and 9834.

Prime Factorization of 9825

Prime Factorization of 9834

Now multiplying the highest exponent prime factors to calculate the LCM of 9825 and 9834.

LCM(9825,9834) = 3¹ × 5² × 131¹ × 2¹ × 11¹ × 149¹
LCM(9825,9834) = 32206350