Question

The H.C.F of two numbers, each having three digits, is 24 and their L.C.M. is 1296. The sum of the numbers will be -​

Answer 1

Step-by-step explanation:

The HCF of two numbers is 17. So,

Let the two numbers be 17x & 17y.

LCM of 17x & 17y.

LCM =17xy.

=> 17xy=714.

=> xy =714/17.

=> 42.

So, Now the factors of 42 are

=> 1×42

=> 2×21

=> 3×14

=> 6×7

So, There are 4 cases.

Case1 :-

Let x=1 & y =42.

Then the numbers will be

=> 17×1=17

=> 17×42= 714.

This condition is not possible. because the From the question, the two numbers are 3-digit numbers .But 17 is a two digit number.

Case2:-

Let x=2 & y =21

The numbers,

=> 17×2=34

=> 17×21=357.

This condition is also not possible. because 34 is a 2-digit number.

Case3:-

Let x=3 & y=14

The numbers,

=> 17×3= 51

=>17×14 =238.

This condition is also not possible.

Case4:-

Let x=6 & y=7

The numbers,

=> 17×6= 102

=>17×7=119.

This is the only condition. that is possible.

So, The sum of the numbers is

=> 102+119

=> 221.

Answer 2

Answer:

714 , 348, 238, 214

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