What is the Least Common Multiple of 67408 and 67414?

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 67408 and 67414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67408 and 67414, than apply into the LCM equation.

GCF(67408,67414) = 2
LCM(67408,67414) = ( 67408 × 67414) / 2
LCM(67408,67414) = 4544242912 / 2
LCM(67408,67414) = 2272121456

Least Common Multiple (LCM) of 67408 and 67414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67408 and 67414. First we will calculate the prime factors of 67408 and 67414.

Prime Factorization of 67408

Prime Factorization of 67414

Now multiplying the highest exponent prime factors to calculate the LCM of 67408 and 67414.

LCM(67408,67414) = 2⁴ × 11¹ × 383¹ × 37¹ × 911¹
LCM(67408,67414) = 2272121456