Question

Find the least number which when divided by 6,15 and 18 leave remainder 5 in each case.

Answer 1

Hint: Here the given question is to find a least number which when divided by the given numbers and leave remainder of five, here we have to use the property of lowest common factor, where we need to take the L.C.M of the given numbers and then add five into it to get the required number.

Complete step-by-step solution:
Here to find the least number with the condition that the required number when divided by 6,15,and 18 will give the remainder of five, so in order to get the required number we need to get the lowest common factor for the given number, on solving we get:
Lowest common factor of the numbers 6,15 and 18 are:
\[\Rightarrow 6 = 2 \times 3 \times 1 \\
   \Rightarrow 15 = 3 \times 5 \times 1 \\
   \Rightarrow 18 = 2 \times 3 \times 3 \times 1 \\
  L.C.M = 2 \times 3 \times 3 \times 5 = 90 \]
Here the required number will be:
\[ \Rightarrow 90 + 5 = 95\]
It is our required number.

Note: Lowest common factor between the numbers are obtained, by multiplying the common factors of the numbers and the factors except the common factor. The product obtained will give the lowest common factor between the numbers.