Question

Find the smallest number which when divided by $15$ and $27$, respectively, leaves a remainder ,$7$ in each case

Answer 1

Step 1: Find the LCM

Given numbers are $15$ and $27$

Prime factors of $15$ are

$15=3\times 5$

Prime factors of $27$ are

$27=3\times 3\times 3$

$\therefore$LCM of $15$ and $27$ is

LCM$\left(15,27\right)=3\times 3\times 3\times 5=135$

Step 2: Find the smallest number which gives remainder.

To get the smallest number, when divided by $15$ and $27$ , gives a remainder $7$, we have to add $7$ to LCM of $15$ and $27$ .

$\therefore 135+7=142$

Hence, the number is $142$.