A number N when divided by 2, 3, 5, 8 and 10 leaves a remainder of 1 in each case. Which of the following could N be? 1. 481 2. 600 3. 119 4. 151 5.221 Answer: Every number can be represented as  Number = divisor x quotient + remainder. Let N be the number N= 2 x quotient1 + 1….(N1)= 2 x quotient1 N= 3 x quotient2 + 1……(N1)= 3 x quotient2 N= 5 x quotient3 + 1……(N1)= 5 x quotient3 N= 8 x quotient4 + 1……(N1)= 8 x quotient3 N= 10 x quotient5 + 1……(N1)= 10 x quotient4 (N1) is the multiple of quotient 1,2,3,4. In fact (N1) is the common multiple of all the numbers 2,3,5,8,10. Hence (N1) can be computed by finding the LCM of 2,3,5,8 and 10. LCM = 480 N1=480, N=481 The number can be 481. 
