GCD & LCM

The Greatest Common Divisor of two numbers is the largest integer that can divide two numbers with a remainder of 0. This can be found by writing a list of all divisors for each number and identifying which integers are divisors for both numbers and simply finding the largest common one, the last divisor they will have in common. (This can also be applied to polynomials) For example:

  The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
  The divisors of 45 are 1, 3, 5, 9, 15, and 45.
  So their common divisors are 1, 3, 5, and 15. Thus, the GCD of 45 and 60 is 15!
(The GCD of two primes will be 1! But the GCD of a prime and it's multiple is the prime number.)

The Least Common Multiple of two numbers is the smallest integer that is a multiple of each number. This can also be found by writing a list of several multiples for each number and identifying inegers which are multiples for both numbers and simply finding the smallest one, the first one they have in common.

  The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120...
  The multiples of 20 are 20, 40, 60, 80, 100, 120...
  So their common multiples are 60, 120, ... We look at the first (lowest) common multiple which is 60.

Here are some GCD and LCM examples to figure out:
GCD
1. 7 and 21
2. 33 and 121
3. 47 and 97
4. 47 and 235
5. 49 and 56

LCM
6. 9 and 12
7. 4 and 62
8. 17 and 21
9. 6 and 75
10. 18 and 24

Answers:
(1) 7, (2) 11, (3) 1, (4) 47, (5) 7, (6) 36, (7) 124, (8) 357, (9) 150, (10) 72

-Zech