Question

The LCM of two numbers is 1024 and one of them is a prime number. Find their HCF.

Answer 1

Hint: Before solving this question first we recall the definitions of LCM, HCF and prime numbers. Then we will find the factors of the number 1024 using prime factorization and then by analyzing the factors obtained we get the desired answer.

Complete step by step solution:
We have been given that the LCM of two numbers is 1024 and one of them is a prime number.
We have to find the HCF of two numbers.
We know that LCM means least common multiple. LCM is defined as the smallest integer which is a multiple of two or more numbers.
Now, we have given that one number is the prime number. We know that the prime number has only two factors as 1 and the number itself.
As the given LCM 1024 is an even number. Let us factorize the number 1024. Then we will get
$1024=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
Now, we know that HCF is the largest common factor of all given numbers.
Now, if one of the numbers is prime then we will get HCF as 2 because 2 is the only even prime number.

Hence HCF of two numbers must be 2.

Note: The relation between LCM and HCF is given as : The product of LCM and HCF is equal to the product of the given numbers. Here in this particular question we don’t have to assume numbers, we have to solve this question numerically by intuitive thinking process.