What is the Least Common Multiple of 43758 and 43776?

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 43758 and 43776 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43758 and 43776, than apply into the LCM equation.

GCF(43758,43776) = 18
LCM(43758,43776) = ( 43758 × 43776) / 18
LCM(43758,43776) = 1915550208 / 18
LCM(43758,43776) = 106419456

Least Common Multiple (LCM) of 43758 and 43776 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43758 and 43776. First we will calculate the prime factors of 43758 and 43776.

Prime Factorization of 43758

Prime Factorization of 43776

Now multiplying the highest exponent prime factors to calculate the LCM of 43758 and 43776.

LCM(43758,43776) = 2⁸ × 3² × 11¹ × 13¹ × 17¹ × 19¹
LCM(43758,43776) = 106419456