Find the greatest common factor and least common multiple of numbers in two ways 520 and 540.

Method 1. Through factorization.

520 = 2 ^ 3 5 13;
540 = 2 2 3 ^ 3 5.
General: 2, 2, 5.
GCD (520; 540) = 2 2 5 = 20.
For the LCM to 540, add the factors 5 and 2 of 520:
LCM (520; 540) = 540 2 13 = 14040.
Method 2. Euclid’s algorithm (step-by-step replacement of a larger number with a difference until equal).
540 and 520: 540 – 520 = 20;
20 and 520: 520 – 20 = 500;
20 and 500: 500 – 20 = 480;
480 and 20: 480 – 20 = 460;
…
20 = 20 is GCD (540; 520).
LCM (540; 520) = 540 520: GCD (540; 520) = 14040.