What is the Least Common Multiple of 69984 and 69990?

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 69984 and 69990 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69984 and 69990, than apply into the LCM equation.

GCF(69984,69990) = 6
LCM(69984,69990) = ( 69984 × 69990) / 6
LCM(69984,69990) = 4898180160 / 6
LCM(69984,69990) = 816363360

Least Common Multiple (LCM) of 69984 and 69990 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69984 and 69990. First we will calculate the prime factors of 69984 and 69990.

Prime Factorization of 69984

Prime Factorization of 69990

Now multiplying the highest exponent prime factors to calculate the LCM of 69984 and 69990.

LCM(69984,69990) = 2⁵ × 3⁷ × 5¹ × 2333¹
LCM(69984,69990) = 816363360