What is the Least Common Multiple of 1400 and 1408?

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 1400 and 1408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1400 and 1408, than apply into the LCM equation.

GCF(1400,1408) = 8
LCM(1400,1408) = ( 1400 × 1408) / 8
LCM(1400,1408) = 1971200 / 8
LCM(1400,1408) = 246400

Least Common Multiple (LCM) of 1400 and 1408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1400 and 1408. First we will calculate the prime factors of 1400 and 1408.

Prime Factorization of 1400

Prime Factorization of 1408

Now multiplying the highest exponent prime factors to calculate the LCM of 1400 and 1408.

LCM(1400,1408) = 2⁷ × 5² × 7¹ × 11¹
LCM(1400,1408) = 246400