What is the Least Common Multiple of 77760 and 77770?

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 77760 and 77770 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77760 and 77770, than apply into the LCM equation.

GCF(77760,77770) = 10
LCM(77760,77770) = ( 77760 × 77770) / 10
LCM(77760,77770) = 6047395200 / 10
LCM(77760,77770) = 604739520

Least Common Multiple (LCM) of 77760 and 77770 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 77760 and 77770. First we will calculate the prime factors of 77760 and 77770.

Prime Factorization of 77760

Prime Factorization of 77770

Now multiplying the highest exponent prime factors to calculate the LCM of 77760 and 77770.

LCM(77760,77770) = 2⁶ × 3⁵ × 5¹ × 7¹ × 11¹ × 101¹
LCM(77760,77770) = 604739520