What is the Least Common Multiple of 37664 and 37674?

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 37664 and 37674 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37664 and 37674, than apply into the LCM equation.

GCF(37664,37674) = 2
LCM(37664,37674) = ( 37664 × 37674) / 2
LCM(37664,37674) = 1418953536 / 2
LCM(37664,37674) = 709476768

Least Common Multiple (LCM) of 37664 and 37674 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37664 and 37674. First we will calculate the prime factors of 37664 and 37674.

Prime Factorization of 37664

Prime Factorization of 37674

Now multiplying the highest exponent prime factors to calculate the LCM of 37664 and 37674.

LCM(37664,37674) = 2⁵ × 11¹ × 107¹ × 3² × 7¹ × 13¹ × 23¹
LCM(37664,37674) = 709476768