What is the Least Common Multiple of 89742 and 89760?

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 89742 and 89760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89742 and 89760, than apply into the LCM equation.

GCF(89742,89760) = 6
LCM(89742,89760) = ( 89742 × 89760) / 6
LCM(89742,89760) = 8055241920 / 6
LCM(89742,89760) = 1342540320

Least Common Multiple (LCM) of 89742 and 89760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89742 and 89760. First we will calculate the prime factors of 89742 and 89760.

Prime Factorization of 89742

Prime Factorization of 89760

Now multiplying the highest exponent prime factors to calculate the LCM of 89742 and 89760.

LCM(89742,89760) = 2⁵ × 3¹ × 14957¹ × 5¹ × 11¹ × 17¹
LCM(89742,89760) = 1342540320