Question

The sum of LCM and HCF of two numbers is 854. If the LCM is 60 times the HCF and one of the numbers is 70, then the other number is:

• A. 160
• B. 164
• C. 168
• D. 172

Answer 1

The Correct Option is C

Let the two numbers be \(a\) and \(b\). We are given that \(a=70\). 

We are also given that LCM + HCF = 854 and LCM = 60 \(\times\) HCF.

Substituting LCM = 60 \(\times\) HCF into the first equation, we get 60 * HCF + HCF = 854, which simplifies to 61 * HCF = 854.

Therefore, HCF = \( \frac{854}{61} = 14 \).

Now, LCM = 60 \(\times\) 14 = 840.

We know that the product of two numbers is equal to the product of their LCM and HCF. So, \(a \times b = LCM \times HCF\).

\(70 \times b = 840 \times 14\)

\(b = \frac{840 \times 14}{70} = \frac{840}{5} = 168\)

Answer 2

Let HCF be $x$, so LCM = $60x$. 
$x + 60x = 854 \Rightarrow 61x = 854 \Rightarrow x = 14$. LCM = $60 \times 14 = 840$. 
The product of the numbers is $70 \times \text{other number} = 14 \times 840$. 
Hence, the other number is 168.