What is the Least Common Multiple of 7824 and 7830?

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 7824 and 7830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7824 and 7830, than apply into the LCM equation.

GCF(7824,7830) = 6
LCM(7824,7830) = ( 7824 × 7830) / 6
LCM(7824,7830) = 61261920 / 6
LCM(7824,7830) = 10210320

Least Common Multiple (LCM) of 7824 and 7830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7824 and 7830. First we will calculate the prime factors of 7824 and 7830.

Prime Factorization of 7824

Prime Factorization of 7830

Now multiplying the highest exponent prime factors to calculate the LCM of 7824 and 7830.

LCM(7824,7830) = 2⁴ × 3³ × 163¹ × 5¹ × 29¹
LCM(7824,7830) = 10210320