What is the Least Common Multiple of 560 and 574?

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 574 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 574, than apply into the LCM equation.

GCF(560,574) = 14
LCM(560,574) = ( 560 × 574) / 14
LCM(560,574) = 321440 / 14
LCM(560,574) = 22960

Least Common Multiple (LCM) of 560 and 574 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 560 and 574. First we will calculate the prime factors of 560 and 574.

Prime Factorization of 560

Prime Factorization of 574

Now multiplying the highest exponent prime factors to calculate the LCM of 560 and 574.

LCM(560,574) = 2⁴ × 5¹ × 7¹ × 41¹
LCM(560,574) = 22960