What is the Least Common Multiple of 37752 and 37760?

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 37752 and 37760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37752 and 37760, than apply into the LCM equation.

GCF(37752,37760) = 8
LCM(37752,37760) = ( 37752 × 37760) / 8
LCM(37752,37760) = 1425515520 / 8
LCM(37752,37760) = 178189440

Least Common Multiple (LCM) of 37752 and 37760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37752 and 37760. First we will calculate the prime factors of 37752 and 37760.

Prime Factorization of 37752

Prime Factorization of 37760

Now multiplying the highest exponent prime factors to calculate the LCM of 37752 and 37760.

LCM(37752,37760) = 2⁷ × 3¹ × 11² × 13¹ × 5¹ × 59¹
LCM(37752,37760) = 178189440