What is the Least Common Multiple of 69408 and 69414?

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 69408 and 69414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69408 and 69414, than apply into the LCM equation.

GCF(69408,69414) = 6
LCM(69408,69414) = ( 69408 × 69414) / 6
LCM(69408,69414) = 4817886912 / 6
LCM(69408,69414) = 802981152

Least Common Multiple (LCM) of 69408 and 69414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69408 and 69414. First we will calculate the prime factors of 69408 and 69414.

Prime Factorization of 69408

Prime Factorization of 69414

Now multiplying the highest exponent prime factors to calculate the LCM of 69408 and 69414.

LCM(69408,69414) = 2⁵ × 3² × 241¹ × 23¹ × 503¹
LCM(69408,69414) = 802981152