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

**(**is divisible by*a*, b )**and***a*and*b***are divisible by HCF***a*and*b***(**.*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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