What is the Least Common Multiple of 9840 and 9850?

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 9840 and 9850 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9840 and 9850, than apply into the LCM equation.

GCF(9840,9850) = 10
LCM(9840,9850) = ( 9840 × 9850) / 10
LCM(9840,9850) = 96924000 / 10
LCM(9840,9850) = 9692400

Least Common Multiple (LCM) of 9840 and 9850 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9840 and 9850. First we will calculate the prime factors of 9840 and 9850.

Prime Factorization of 9840

Prime Factorization of 9850

Now multiplying the highest exponent prime factors to calculate the LCM of 9840 and 9850.

LCM(9840,9850) = 2⁴ × 3¹ × 5² × 41¹ × 197¹
LCM(9840,9850) = 9692400