What is the Least Common Multiple of 1408 and 1414?

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 1408 and 1414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1408 and 1414, than apply into the LCM equation.

GCF(1408,1414) = 2
LCM(1408,1414) = ( 1408 × 1414) / 2
LCM(1408,1414) = 1990912 / 2
LCM(1408,1414) = 995456

Least Common Multiple (LCM) of 1408 and 1414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1408 and 1414. First we will calculate the prime factors of 1408 and 1414.

Prime Factorization of 1408

Prime Factorization of 1414

Now multiplying the highest exponent prime factors to calculate the LCM of 1408 and 1414.

LCM(1408,1414) = 2⁷ × 11¹ × 7¹ × 101¹
LCM(1408,1414) = 995456