What is the Least Common Multiple of 49152 and 49170?

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 49152 and 49170 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49152 and 49170, than apply into the LCM equation.

GCF(49152,49170) = 6
LCM(49152,49170) = ( 49152 × 49170) / 6
LCM(49152,49170) = 2416803840 / 6
LCM(49152,49170) = 402800640

Least Common Multiple (LCM) of 49152 and 49170 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49152 and 49170. First we will calculate the prime factors of 49152 and 49170.

Prime Factorization of 49152

Prime Factorization of 49170

Now multiplying the highest exponent prime factors to calculate the LCM of 49152 and 49170.

LCM(49152,49170) = 2¹⁴ × 3¹ × 5¹ × 11¹ × 149¹
LCM(49152,49170) = 402800640