1. the lcm of two numbers is 504.Which of the following numbers cannot be the hcf of these numbers? 16; 1`8; 42; 36

Please explain.

 

2.in which of the following cases the construction of a triangle is possible, the length of sides given [in cm]as: 

a. 14; 19; 5                  b. 18; 12; 5               c. 12; 6;9            d. 8; 4; 12

please explain

             

Hi!
Here is the answer to your question.
 
(i)
Let the two numbers be a and b.
LCM (a , b )  is divisible by a and b and a and b are divisible by HCF(a , b ).
∴ LCM is divisible by HCF.
Given, LCM = 504
From the given options, 16 do not divide 504.
∴ HCF of two numbers can not by 16.
(ii)
In a triangle, the sum of any two sides of a triangle is greater than the third side.
Consider the sides of the triangle given in option (C).
12 + 6 = 18 > 9
6 + 9 = 15 > 12
12 + 9 = 21 > 6
∴ It is possible to construct triangle whose sides are 12, 6 and 9.
 
Cheers!

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Thanks so much for clearing my concepts. Meritnation is really helping me a lot in my studies

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