What is the Least Common Multiple of 34540 and 34560?

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 34540 and 34560 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34540 and 34560, than apply into the LCM equation.

GCF(34540,34560) = 20
LCM(34540,34560) = ( 34540 × 34560) / 20
LCM(34540,34560) = 1193702400 / 20
LCM(34540,34560) = 59685120

Least Common Multiple (LCM) of 34540 and 34560 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34540 and 34560. First we will calculate the prime factors of 34540 and 34560.

Prime Factorization of 34540

Prime Factorization of 34560

Now multiplying the highest exponent prime factors to calculate the LCM of 34540 and 34560.

LCM(34540,34560) = 2⁸ × 5¹ × 11¹ × 157¹ × 3³
LCM(34540,34560) = 59685120