What is the Least Common Multiple of 49140 and 49152?

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 49140 and 49152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49140 and 49152, than apply into the LCM equation.

GCF(49140,49152) = 12
LCM(49140,49152) = ( 49140 × 49152) / 12
LCM(49140,49152) = 2415329280 / 12
LCM(49140,49152) = 201277440

Least Common Multiple (LCM) of 49140 and 49152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49140 and 49152. First we will calculate the prime factors of 49140 and 49152.

Prime Factorization of 49140

Prime Factorization of 49152

Now multiplying the highest exponent prime factors to calculate the LCM of 49140 and 49152.

LCM(49140,49152) = 2¹⁴ × 3³ × 5¹ × 7¹ × 13¹
LCM(49140,49152) = 201277440