Question

Find the least number which when divided by 615 and 18 leaves remainder 3 in each case​

Answer 1

$\textbf{\underline{Answer :-}}$

The number when divided by 615 and 18 leaves remainder 3 is 3693.

$\textbf{\underline{Explanation :-}}$

$\textsf{\underline{Given :-}}$

The two numbers = 615 and 18

The remainder wanted = 3

$\textsf{\underline{To find :-}}$

The least number which divided by 615 and 18 leaves remainder 3

$\textsf{\underline{Solution :-}}$

$\textsf{Step 1 :}$

Find the LCM of 615 and 18

LCM =

$\begin{array}{r|l}3 & 615,18 \\\cline{1-2} 5 & 205,6 \\\cline{1-2} 41 & 41 , 6\\ \cline{1-2} 2 & 1 , 6 \\\cline{1-2} 3&1 , 3\\\cline{1-2} &1 , 1\end{array}$

LCM = 3 × 5 × 41 × 2 × 3

LCM = 3,690

Therefore 3,690 is the least number which divided by 615 and 18 leaves no remainder.

$\textsf{Step 2 : Add 3 to LCM}$

According to the question, the reminder should be 3

So,

$\tt{\Rightarrow3690 + 3}$

$\tt{\Rightarrow3693}$

$\therefore$The number when divided by 615 and 18 leaves remainder 3 is 3693.

$\textsf{\underline{Verification :-}}$

$\tt{\Rightarrow \: 3693 \div 615}$

$\tt{\Rightarrow \: Quotient \: = 6}$

$\tt{\Rightarrow \: Remainder = 3}$

$\tt{\Rightarrow3693 \div 18}$

$\tt{\Rightarrow \: Quotient \: = 205}$

$\tt{\Rightarrow \: Remainder = 3}$

Both the numbers when divide 3693 leave remainder 3

$\therefore$The number when divided by 615 and 18 leaves remainder 3 is 3693.