find the smallest possible value of a whole number Y if it leaves a remainder of 3 when divided by 5,6 or 9

Question

find the smallest possible value of a whole number Y if it leaves a remainder of 3 when divided by 5,6 or 9

 

find the smallest possible value of a whole number X if it leaves a remainder of 2 when divided by 4,3 or 6

Answer 1

Do a primate factorization of the numbers in each set to find the least common multiple:

 

5 (prime), 6 = 2 x 3, 9 = 3 x 3

 

The LCM is 5 x 2 x 3 x 3 = 90.  Now add 3 to this to give the desired remainder  (93).

 

Use the same procedure for the second item:

 

4 = 2 x 2, 3 (prime), 6 = 2 x 3

 

The LCM is 2 x 2 x 3 = 12.  Add to to get the remainder.  Your target number is 14.