What is the Least Common Multiple of 550 and 565?

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 550 and 565 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 550 and 565, than apply into the LCM equation.

GCF(550,565) = 5
LCM(550,565) = ( 550 × 565) / 5
LCM(550,565) = 310750 / 5
LCM(550,565) = 62150

Least Common Multiple (LCM) of 550 and 565 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 550 and 565. First we will calculate the prime factors of 550 and 565.

Prime Factorization of 550

Prime Factorization of 565

Now multiplying the highest exponent prime factors to calculate the LCM of 550 and 565.

LCM(550,565) = 2¹ × 5² × 11¹ × 113¹
LCM(550,565) = 62150