What is the Least Common Multiple of 20160 and 20174?

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 20160 and 20174 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20160 and 20174, than apply into the LCM equation.

GCF(20160,20174) = 14
LCM(20160,20174) = ( 20160 × 20174) / 14
LCM(20160,20174) = 406707840 / 14
LCM(20160,20174) = 29050560

Least Common Multiple (LCM) of 20160 and 20174 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20160 and 20174. First we will calculate the prime factors of 20160 and 20174.

Prime Factorization of 20160

Prime Factorization of 20174

Now multiplying the highest exponent prime factors to calculate the LCM of 20160 and 20174.

LCM(20160,20174) = 2⁶ × 3² × 5¹ × 7¹ × 11¹ × 131¹
LCM(20160,20174) = 29050560