What is the Least Common Multiple of 38160 and 38174?

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 38160 and 38174 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38160 and 38174, than apply into the LCM equation.

GCF(38160,38174) = 2
LCM(38160,38174) = ( 38160 × 38174) / 2
LCM(38160,38174) = 1456719840 / 2
LCM(38160,38174) = 728359920

Least Common Multiple (LCM) of 38160 and 38174 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38160 and 38174. First we will calculate the prime factors of 38160 and 38174.

Prime Factorization of 38160

Prime Factorization of 38174

Now multiplying the highest exponent prime factors to calculate the LCM of 38160 and 38174.

LCM(38160,38174) = 2⁴ × 3² × 5¹ × 53¹ × 19087¹
LCM(38160,38174) = 728359920