What is the Least Common Multiple of 45696 and 45705?

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 45696 and 45705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45696 and 45705, than apply into the LCM equation.

GCF(45696,45705) = 3
LCM(45696,45705) = ( 45696 × 45705) / 3
LCM(45696,45705) = 2088535680 / 3
LCM(45696,45705) = 696178560

Least Common Multiple (LCM) of 45696 and 45705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45696 and 45705. First we will calculate the prime factors of 45696 and 45705.

Prime Factorization of 45696

Prime Factorization of 45705

Now multiplying the highest exponent prime factors to calculate the LCM of 45696 and 45705.

LCM(45696,45705) = 2⁷ × 3¹ × 7¹ × 17¹ × 5¹ × 11¹ × 277¹
LCM(45696,45705) = 696178560