What is the Least Common Multiple of 49000 and 49008?

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 49000 and 49008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49000 and 49008, than apply into the LCM equation.

GCF(49000,49008) = 8
LCM(49000,49008) = ( 49000 × 49008) / 8
LCM(49000,49008) = 2401392000 / 8
LCM(49000,49008) = 300174000

Least Common Multiple (LCM) of 49000 and 49008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49000 and 49008. First we will calculate the prime factors of 49000 and 49008.

Prime Factorization of 49000

Prime Factorization of 49008

Now multiplying the highest exponent prime factors to calculate the LCM of 49000 and 49008.

LCM(49000,49008) = 2⁴ × 5³ × 7² × 3¹ × 1021¹
LCM(49000,49008) = 300174000