What is the Least Common Multiple of 7830 and 7842?

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 7830 and 7842 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7830 and 7842, than apply into the LCM equation.

GCF(7830,7842) = 6
LCM(7830,7842) = ( 7830 × 7842) / 6
LCM(7830,7842) = 61402860 / 6
LCM(7830,7842) = 10233810

Least Common Multiple (LCM) of 7830 and 7842 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7830 and 7842. First we will calculate the prime factors of 7830 and 7842.

Prime Factorization of 7830

Prime Factorization of 7842

Now multiplying the highest exponent prime factors to calculate the LCM of 7830 and 7842.

LCM(7830,7842) = 2¹ × 3³ × 5¹ × 29¹ × 1307¹
LCM(7830,7842) = 10233810