Question

find the smallest 4 digit number which is exactly divisible by 12,24 and 32​

Answer 1

Answer:

1152

Step-by-step-explaination

Given :

Numbers 12 , 24 , 32

To Find :

A 4 digit number that will divide 12, 24, 32 exactly.

Procedure :

Find the LCM of 12, 24, 32

${\begin{array}{r | l}12 & 12,24,32 \\\cline{2-2} 2 & 1,2,32 \\\cline{2-2} & 1,1,16 \\ \end{array}$

$\implies \sf \: 12 \times 2 \times 16$

$\implies \: 24 \times 16$

$\implies \: 384$

Now , The smallest number divisible by 12,24,32 is 384.

But in question it has asked to find the smallest 4 digit number that would be divisible by 12 , 24 , 32.

From these , We can infer that , we need to have a smallest 4 digit number. We also know that , smallest 4 digit number is 1000.

Next , divide 1000 by 384.

Divisor = 384

Dividend = 1000

Quotient = 2

Remainder = 232.

We get remainder as 232.

In order to get the smallest 3 digit number , we need to nullify remainder completely divide it by 1000.

We know that

$\sf \: quotient \: \times divisor + remainder \: = dividend$

$\sf \: 2 \: \times 384 + 232 \: = 1000$

If we make 232 as zero , we will be able to divide it completely.

For this, we will simply subtract 232 from 384.

$\sf \: smallest \: 4 - digit \: number = 1000 + (384 - 232)$

$\sf smallest \: 4 - digit \: number = 1000 + 152$

$\sf \: smallest \: 4 - digit \: number = 1152$