Question

What is the least number which when divided by the numbers 3,5,6,8,10,12 leaves in each case a reminder 2 but when divided by 13 leaves no remainder?

Answer 1

Answer:

962

Step-by-step explanation:

Here's how you approach such questions. First find the lcm of the numbers that the required number is divisible with, i.e., 3,5,6,8,10,12 which is 120

Therefore the required number is of the form 120x+2 (since it leaves a reminder of 2)

Now the number is a multiple of 13.  

so 120x+2 is a multiple of 13

=> 117x + 3x+2 is a multiple of 13

The least value of x for which this holds true is 8 (3*8+2 = 26)

Therefore the least such number is 120*8+2 = 962

Answer 2

Answer:

962

Step-by-step explanation:

Here's how you approach such questions. First find the lcm of the numbers that the required number is divisible with, i.e., 3,5,6,8,10,12 which is 120

Therefore the required number is of the form 120x+2 (since it leaves a reminder of 2)

Now the number is a multiple of 13.  

so 120x+2 is a multiple of 13

=> 117x + 3x+2 is a multiple of 13