Question

What is the smallest number which has a reminder of 2 when it is divided by 6,7 and 8

Answer 1

170 is the smallest number which has a reminder of 2 when it is divided by 6,7 and 8

Explanation:

The Least or Lowest Common Multiple (LCM) or Least Common Divisor (LCD).

For two integers a and b, denoted LCM (a, b), the LCM is the smallest positive integer that is evenly divisible by both a and b. The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set. Let find LCM of 6, 7 and 8.

`6=2 * 3`

`8=2 * 2 * 2`

`7=7 * 1`

`L C M=2 * 2 * 2 * 3 * 7=168`

We add 2 to LCM to get the smallest number which gives a remainder of 2.

So, the number is 168+ 2 = 170