What is the Least Common Multiple of 37740 and 37749?

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 37749 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 37749, than apply into the LCM equation.

GCF(37740,37749) = 3
LCM(37740,37749) = ( 37740 × 37749) / 3
LCM(37740,37749) = 1424647260 / 3
LCM(37740,37749) = 474882420

Least Common Multiple (LCM) of 37740 and 37749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37740 and 37749. First we will calculate the prime factors of 37740 and 37749.

Prime Factorization of 37740

Prime Factorization of 37749

Now multiplying the highest exponent prime factors to calculate the LCM of 37740 and 37749.

LCM(37740,37749) = 2² × 3¹ × 5¹ × 17¹ × 37¹ × 12583¹
LCM(37740,37749) = 474882420