What is the Least Common Multiple of 89760 and 89765?

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 89760 and 89765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89760 and 89765, than apply into the LCM equation.

GCF(89760,89765) = 5
LCM(89760,89765) = ( 89760 × 89765) / 5
LCM(89760,89765) = 8057306400 / 5
LCM(89760,89765) = 1611461280

Least Common Multiple (LCM) of 89760 and 89765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89760 and 89765. First we will calculate the prime factors of 89760 and 89765.

Prime Factorization of 89760

Prime Factorization of 89765

Now multiplying the highest exponent prime factors to calculate the LCM of 89760 and 89765.

LCM(89760,89765) = 2⁵ × 3¹ × 5¹ × 11¹ × 17¹ × 13¹ × 1381¹
LCM(89760,89765) = 1611461280