Question

the least number which when divided by 6, 9, 12, 15, 18 leaving same remainder 2 in each case is​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The number is 182 which when is divided by 6,9,12,15 and 18 leaves Remainder as 2 in each case.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

$\textbf{Given :}$

The numbers = 6, 9, 12, 15, 18

$\textbf{To find :}$

A number which when divided by the numbers leave Remainder 2 in each case.

$\textbf{Solution : }$

First we need to find the LCM of 6,9,12,15 and 18

$\begin{array}{r|l} 2 & 6,9,12,15,18 \\\cline{1-2} 3 & 3,9,6,15,9 \\\cline{1-2} 3 & 1,3,2,5,3 \\ \cline{1-2} 2 & 1,1,2,5,1 \\\cline{1-2} 5 & 1,1,1,5,1 \\\cline{1-2} & 1,1,1,1,1 \end{array}$

LCM = 2 × 3 × 3 × 2 × 5 = 180

We got the LCM as 180

Add 2 to it.

$\implies$ 180 + 2

$\implies$ 182

$\therefore$ The number is 182 which when is divided by 6,9,12,15 and 18 leaves Remainder as 2 in each case.

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\implies$ 182 ÷ 6

Quotient : 30

Remainder : 2

$\implies$ 182 ÷ 9

Quotient : 20

Remainder : 2

$\implies$ 182 ÷ 12

Quotient : 15

Remainder : 2

$\implies$ 182 ÷ 15

Quotient : 12

Remainder : 2

$\implies$ 182 ÷ 18

Quotient : 10

Remainder : 2

$\therefore$ The number is 182 which when is divided by 6,9,12,15 and 18 leaves Remainder as 2 in each case.

Answer 2

Answer:

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Step-by-step explanation:

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