Question

find the smallest number which when 4
divided by 12, 18 and 32 leaves remainder
5 in each case.​

Answer 1

AnswEr :

$\bf{\orange{\underline{\underline{\bf{Given\::}}}}}$

Which when 4 divided by 12, 18, 32 leaves remainder 5 in each case.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The smallest number.

$\bf{\purple{\underline{\underline{\bf{Explanation\::}}}}}$

We get L.C.M of 12, 18, 32 are :

$\begin{array}{l|r} \cline{2-2} 2& 12,18,32 \\ \cline{2-2} 2& 6,9,16\\ \cline{2-2} 2 & 3,9, 8\\ \cline{2-2} 2 & 3,9,4\\ \cline{2-2} 2& 3,9,2\\ \cline{2-2} 3& 3,9,1\\ \cline{ 2-2} 3& 1,3,1\\ \cline{2-2} & 1,1,1\end{array}}$

∴ L.C.M = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.

$\bf{\large{\underline{\sf{Required\:number\:=288+5=293.}}}}}$

&

The smallest number which leaves remainder 4, we get;

$\leadsto\sf{Smallest\:number\:=\:293-4}}\\\\\leadsto\sf{\red{Smallest\:number\:=\:289}}$

$\therefore$$\bf{\large{\red{\underline{\sf{The\:smallest\:number\:is\:289.}}}}}$

Answer 2

Correct Question:

Find the smallest number which when

divided by 12, 18 and 32 leaves remainder

5 in each case.

Answer:

$\large\boxed{\sf{293}}$

Step-by-step explanation:

According to question,

We have to find the smallest number which when divided by 12, 18 and 32 leaves remainder 5 in each case

For this, we need to find the LCM of 12, 18 and 32.

Now, to find the LCM of 12, 18, 32

All prime factors for each number is needed.

=> Prime Factorization of 12 is:  2 x 2 x 3

=> Prime Factorization of 18 is:  2 x 3 x 3  

=> Prime Factorization of 32 is:  2 x 2 x 2 x 2 x 2

Now, for each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

So, we have the following prime factors required.

2, 2, 2, 2, 2, 3, 3

Now, multiply these factors together to find the LCM.

=> LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288

Therefore, we will get

=> Smallest number = (LCM of 12, 18, 32 ) + 5

=> Smallest number = 288 + 5 = 293

Hence, the smallest number which when divided by 12 18 and 32 leaves remainder 5 in each case is 293