What is the Least Common Multiple of 34720 and 34740?

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 34720 and 34740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34720 and 34740, than apply into the LCM equation.

GCF(34720,34740) = 20
LCM(34720,34740) = ( 34720 × 34740) / 20
LCM(34720,34740) = 1206172800 / 20
LCM(34720,34740) = 60308640

Least Common Multiple (LCM) of 34720 and 34740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34720 and 34740. First we will calculate the prime factors of 34720 and 34740.

Prime Factorization of 34720

Prime Factorization of 34740

Now multiplying the highest exponent prime factors to calculate the LCM of 34720 and 34740.

LCM(34720,34740) = 2⁵ × 5¹ × 7¹ × 31¹ × 3² × 193¹
LCM(34720,34740) = 60308640