How to determine the lcd for 3/4,7/12,5/6,1/5 by inspection and by division of prime numbers.

not sure what by inspection means, I usually just do it by doing a quick prime factoring of all factors, in this case the denominators.

so we have the denominators of 4, 12, 6 and 5. Let's first find the LCD of 4 and 12.

4 = 2 * 2

12 = 2 * 2 * 3

so the 2 is there twice in the 4 and twice in the 12, so we use it only once, and then we have the 3 there, so the LCD of those two is 2 * 2 * 3, or 12.

now let's find the LCD of that 12 and 6.

12 = 2 * 2 * 3

6 = 2 * 3

so the 2 and 3 is common to both, so we use it only once, and then we have the extra 2. So their LCD is 2 * 3 * 2, or 12 still.

now let's check the LCD of that 12 and 5.

12 = 2 * 2 * 3

5 = 5 < - tis prime

so they have no factors in common, darn, so we use 2 and 2 and 3 and also the 5, so 2 * 2 * 3 * 5 = 60.

and that is the LCD.