What is the Least Common Multiple of 37740 and 37752?

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 37740 and 37752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37740 and 37752, than apply into the LCM equation.

GCF(37740,37752) = 12
LCM(37740,37752) = ( 37740 × 37752) / 12
LCM(37740,37752) = 1424760480 / 12
LCM(37740,37752) = 118730040

Least Common Multiple (LCM) of 37740 and 37752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37740 and 37752. First we will calculate the prime factors of 37740 and 37752.

Prime Factorization of 37740

Prime Factorization of 37752

Now multiplying the highest exponent prime factors to calculate the LCM of 37740 and 37752.

LCM(37740,37752) = 2³ × 3¹ × 5¹ × 17¹ × 37¹ × 11² × 13¹
LCM(37740,37752) = 118730040