Question

The LCM of three different numbers is 1024. Which one of the following can never be there HCF?

Answer 1

Answer:

The LCM of three different number is 1024.

1024 should be divisible by all the given number, if any (as u didn't mentioned options here) number which is not dividing 1024 that can never be there HCF.

Explanation:

The LCM of three different numbers is 1024. Which one of the following can never be their HCF?

A) 91 b) 124 c) 137 d) 140​

Correct Option: 140

Answer 2

CORRECT QUESTION

The LCM of three different numbers is 1024. Which one of the following can never be there HCF?

(a) 8.

(b) 32

(c) 124

(d) 256

ANSWER

The correct answer is option (c) 124.

GIVEN

The LCM of three different numbers is 1024.

TO FIND

The number which can not be the HCF of the three numbers.

SOLUTION

We can simply solve the above problem as follows;

Let the number be, X, Y, and Z.

We know that LCM is the least common multiple of three numbers and HCF is the highest common factor of the given three numbers.

LCM of X, Y, and Z = 1024.

Let A be the Highest common factor of X, Y, and Z.

This means that A exactly divides X, Y, and Z.

So, A will also exactly divide The LCM of the numbers.

Therefore,

Dividing 1024 by 8 = Leaves no remainder.

Dividing 1024 by 32 = Leaves no remainder.

Dividing 1024 by 124 = leaves a non-zero remainder.

Dividing 1024 by 256 = Leaves no remainder.

We can observe that 124 does not divide the LCM of the three numbers.

Hence, 124 cannot be the HCF of the three numbers.

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