Question

If HCF of two
numbers be 40 then which of the following
cannot be their LCM. यदि दो संख्याओं का म.स.व.
40 हो तो इन में से कौन सा ल.स.व. नहीं हो सकता?

20
40
80
160​

Answer 1

Given :- If HCF of two numbers be 40 then which of the following cannot be their LCM. यदि दो संख्याओं का म.स.व. 40 हो तो इन में से कौन सा ल.स.व. नहीं हो सकता?

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

HELLO DEAR,

GIVEN:-If HCF of two number be 40 ,then which of following is can not be their LCM.

A) 20

B) 40

C)80

D)160

SOLUTION:-

The correct option is (A) 20

HCF- ( Highest Common Factor):- Greatest common divisor of two or more integers ,which are not all zero, is the largest positive integer that divide each of the integers.

Ex- HCF of 10 and 20

= 10.

LCM-( Least Common Multiple) :- LCM stand for least common multiple ,multiple is a number you get when you multiply a number by a whole number.

Therefore from above conclusion we can say that LCM will alaway greater tha HCF of the number.

So, LCM of the number whose HCF is 40 will always greater that 40 .

Therefore correct for this question is option (A) 20.

I HOPE IT'S HELP YOU DEAR,

THANKS.