What is the Least Common Multiple of 49824 and 49830?

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 49824 and 49830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49824 and 49830, than apply into the LCM equation.

GCF(49824,49830) = 6
LCM(49824,49830) = ( 49824 × 49830) / 6
LCM(49824,49830) = 2482729920 / 6
LCM(49824,49830) = 413788320

Least Common Multiple (LCM) of 49824 and 49830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49824 and 49830. First we will calculate the prime factors of 49824 and 49830.

Prime Factorization of 49824

Prime Factorization of 49830

Now multiplying the highest exponent prime factors to calculate the LCM of 49824 and 49830.

LCM(49824,49830) = 2⁵ × 3² × 173¹ × 5¹ × 11¹ × 151¹
LCM(49824,49830) = 413788320