170 is the smallest number which has a reminder of 2 when it is divided by 6,7 and 8
Step-by-step 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.
[tex]6=2 \times 3[/tex]
[tex]8=2 \times 2 \times 2[/tex]
[tex]7=7 \times 1[/tex]
[tex]L C M=2 \times 2 \times 2 \times 3 \times 7=168[/tex]
We add 2 to LCM to get the smallest number which gives a remainder of 2.
So, the number is 168+ 2 = 170
