What is the Least Common Multiple of 37408 and 37414?

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 37408 and 37414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37408 and 37414, than apply into the LCM equation.

GCF(37408,37414) = 2
LCM(37408,37414) = ( 37408 × 37414) / 2
LCM(37408,37414) = 1399582912 / 2
LCM(37408,37414) = 699791456

Least Common Multiple (LCM) of 37408 and 37414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37408 and 37414. First we will calculate the prime factors of 37408 and 37414.

Prime Factorization of 37408

Prime Factorization of 37414

Now multiplying the highest exponent prime factors to calculate the LCM of 37408 and 37414.

LCM(37408,37414) = 2⁵ × 7¹ × 167¹ × 13¹ × 1439¹
LCM(37408,37414) = 699791456