What is the Least Common Multiple of 37674 and 37680?

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 37674 and 37680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37674 and 37680, than apply into the LCM equation.

GCF(37674,37680) = 6
LCM(37674,37680) = ( 37674 × 37680) / 6
LCM(37674,37680) = 1419556320 / 6
LCM(37674,37680) = 236592720

Least Common Multiple (LCM) of 37674 and 37680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37674 and 37680. First we will calculate the prime factors of 37674 and 37680.

Prime Factorization of 37674

Prime Factorization of 37680

Now multiplying the highest exponent prime factors to calculate the LCM of 37674 and 37680.

LCM(37674,37680) = 2⁴ × 3² × 7¹ × 13¹ × 23¹ × 5¹ × 157¹
LCM(37674,37680) = 236592720