How do you find out gcf (greatest common factor) and lcm (least common multiple)?

To find the GCF, first you must factor the 2 or more numbers. The GCF is the highest factor the numbers have in common. for example: you have 12 and 8. If you factor out the numbers for 12, you get
1,2,3,4,6,12
For 8, you get:
1,2,4,8
the GCF of this pair is 4 because it is the highest number that goes into both 8 and 12.
To find the LCM, you must find the first number that was multiplied and it must be the same. lets take 3 and 5. Multiply 3 by as many numbers you can think of. For now, lets just go up to 10.
3, 6, 9, 12 15, 18, 21, 24, 27, 30
now to the same for 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
in both 3 and 5, the first set of numbers that match in 30- therefore the LCM of 3 and 5 in 30. I hope this helps!