Question

The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14 the larger of the two number is
$\left( a \right)$ 276
$\left( b \right)$ 299
$\left( c \right)$ 345
$\left( d \right)$ 322

Answer 1

Hint: In this particular question use the concept that HCF of any two or more than two numbers are the product of common factors i.e. the product of number of factors which are same in both the numbers, and LCM of any two or more than two numbers is the smallest integer which is divisible by both the numbers, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14.
As we all know that the HCF of any two or more than two numbers is the product of common factors i.e. the product of a number of factors which are the same in both the numbers.
And we all know that the LCM of any two or more than two numbers is the smallest integer which is divisible by both the numbers, for example LCM of 4 and 6 are 12, which is the smallest integer which is divisible by 4 and 6.
Let first number be x and second number be y
Now it is given that the HCF of two numbers is 23.
So 23 is present in both the numbers.
And the other two factors of their LCM are 13 and 14.
So 13 is present in one number and 14 is present in another number.
Let 13 be present in number x and 14 be present in number y.
So, $x = 23 \times 13$
And
$y = 23 \times 14$
So as we see that number y is largest.
So. Simplify y we have,
$ \Rightarrow y = 23 \times 14 = 322$
So this is the required answer.

So, the correct answer is “Option d”.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the definitions of LCM as well as HCF which is all stated above, so the HCF number is present in both the number and one of the LCM factor is present in one number and other LCM factor is present in another number.