What is the Least Common Multiple of 560 and 578?

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 560 and 578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 560 and 578, than apply into the LCM equation.

GCF(560,578) = 2
LCM(560,578) = ( 560 × 578) / 2
LCM(560,578) = 323680 / 2
LCM(560,578) = 161840

Least Common Multiple (LCM) of 560 and 578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 560 and 578. First we will calculate the prime factors of 560 and 578.

Prime Factorization of 560

Prime Factorization of 578

Now multiplying the highest exponent prime factors to calculate the LCM of 560 and 578.

LCM(560,578) = 2⁴ × 5¹ × 7¹ × 17²
LCM(560,578) = 161840