Question

if HCF of two numbers be 40 then which of the following
cannot be their LCM
20
40
80
160​

Answer 1

Given :- If HCF of two numbers be 40 then which of the following cannot be their LCM. ?

A) 20

B) 40

C) 80

D) 160

Solution :-

we know that,

• HCF(Highest Common Factor) :- The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. Also known as GCD (Greatest Common Divisor).

• LCM(Least Common Multiple) :- The least or smallest common multiple of any two or more given natural numbers are termed as LCM.

• The H.C.F. of given numbers is not greater than any of the numbers.

• The L.C.M. of given numbers is not less than any of the given numbers.

• If a number, say x, is a factor of another number, say y, then the H.C.F. of x and y is x and their L.C.M. is y.

• HCF of a given number always divides its LCM.

given that,

HCF of two numbers = 40

So, checking Options now, we get,

• 20(LCM) is not divisible by 40(HCF) .
• 40(LCM) is divisible by 40(HCF) .
• 80(LCM) is divisible by 40(HCF) .
• 160(LCM) is divisible by 40(HCF) .

Therefore, we can conclude that, 20 (Option A) cannot be their LCM.

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Answer 2

$\sf \underline{SOLUTION} :$

TO CHOOSE THE CORRECT OPTION

If HCF of two numbers be 40 then which of the following cannot be their LCM

• 20

• 40

• 80

• 160

CONCEPT TO BE IMPLEMENTED

HCF

Full form of HCF is Highest Common Factor

For a given set of numbers, the HCF is defined as the highest common factor of the given numbers

For example, 2 is the HCF of 4 and 6

LCM

Full form of LCM is Least Common Multiple

For a given set of numbers, the LCM is defined as the least common multiple of the given numbers

For example, 12 is the LCM of 4 and 6

DEDUCTION

Thus it is obvious that for any two given numbers, their HCF must be a factor of LCM

In other words for any two given numbers, their LCM must be divisible by HCF

EVALUATION

Here it is given that HCF of two numbers be 40

Now check for options

CHECKING FOR OPTION 1

Since 20 is not divisible by 40

So this option is correct

CHECKING FOR OPTION 2

Since 40 is divisible by 40

So this option is not correct

CHECKING FOR OPTION 3

Since 80 is divisible by 40

So this option is not correct

CHECKING FOR OPTION 4

Since 160 is divisible by 40

So this option is not correct

FINAL ANSWER

The correct option is 20

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