What is the Least Common Multiple of 49125 and 49140?

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 49125 and 49140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49125 and 49140, than apply into the LCM equation.

GCF(49125,49140) = 15
LCM(49125,49140) = ( 49125 × 49140) / 15
LCM(49125,49140) = 2414002500 / 15
LCM(49125,49140) = 160933500

Least Common Multiple (LCM) of 49125 and 49140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49125 and 49140. First we will calculate the prime factors of 49125 and 49140.

Prime Factorization of 49125

Prime Factorization of 49140

Now multiplying the highest exponent prime factors to calculate the LCM of 49125 and 49140.

LCM(49125,49140) = 3³ × 5³ × 131¹ × 2² × 7¹ × 13¹
LCM(49125,49140) = 160933500