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Two natural numbers X and Y are such that LCM (X, Y) is 2" x 36 x 7º and HCF
(X, Y) is 2 x 7". Choose the correct statements.
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3 is a factor of both X and Y.
3 is either a factor of X or a factor of Y.
X and Y are both multiples of 7.
Answers
Given : Two natural numbers X and Y are such that LCM (X, Y) is 2 x 36 x 7 and HCF (X, Y) is 2 x 7
To find : Choose correct Statements
Solution:
LCM ( X , Y ) = 2 * 36 * 7
HCF ( X , Y ) = 2 * 7
Let say two numbers are
X & Y are 2 * 7 * a & 2 * 7 * b
where a & b are co prime
X * Y = LCM ( X, Y) * HCF ( X , Y )
=> 2 * 7 * a * 2 * 7 * b = 2 * 36 * 7 * 2 * 7
=> ab = 36
36 = 1 * 36 36 = 4 * 9
( 2 * 18 , 3 * 12 & 6 * 6 are not co prime )
Possible numbers are
14 , 14 * 36 or 14 * 4 & 14 * 9
3 is a factor of both X and Y. - Incorrect as it not in HCF ( X , Y )
3 is either a factor of X or a factor of Y - CORRECT as 3 is a Factor in LCM ( X , Y)
X and Y are both multiples of 7. - CORRECT as 7 is a factor in HCF ( X , Y )
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