What is the Least Common Multiple of 45360 and 45370?

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 45360 and 45370 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45360 and 45370, than apply into the LCM equation.

GCF(45360,45370) = 10
LCM(45360,45370) = ( 45360 × 45370) / 10
LCM(45360,45370) = 2057983200 / 10
LCM(45360,45370) = 205798320

Least Common Multiple (LCM) of 45360 and 45370 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45360 and 45370. First we will calculate the prime factors of 45360 and 45370.

Prime Factorization of 45360

Prime Factorization of 45370

Now multiplying the highest exponent prime factors to calculate the LCM of 45360 and 45370.

LCM(45360,45370) = 2⁴ × 3⁴ × 5¹ × 7¹ × 13¹ × 349¹
LCM(45360,45370) = 205798320