What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18…
What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?
1063
1073
1083
1183
Solution
The LCM of 6, 9, 12, 15 and 18 is 180. The smallest multiple of 180 greater than 1000 is 1080. Adding the remainder 3 gives the required number = 1080 + 3 = 1083.