What is the Least Common Multiple of 49200 and 49205?

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 49200 and 49205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49200 and 49205, than apply into the LCM equation.

GCF(49200,49205) = 5
LCM(49200,49205) = ( 49200 × 49205) / 5
LCM(49200,49205) = 2420886000 / 5
LCM(49200,49205) = 484177200

Least Common Multiple (LCM) of 49200 and 49205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49200 and 49205. First we will calculate the prime factors of 49200 and 49205.

Prime Factorization of 49200

Prime Factorization of 49205

Now multiplying the highest exponent prime factors to calculate the LCM of 49200 and 49205.

LCM(49200,49205) = 2⁴ × 3¹ × 5² × 41¹ × 13¹ × 757¹
LCM(49200,49205) = 484177200