To address this problem, we will establish variables and equations from the provided data.
Let \( H \) represent the HCF of the two numbers and \( L \) represent their LCM. The problem provides the following information:
By substituting \( L = 60H \) into the second equation, we get:
\( 60H + H = 854 \)
\( 61H = 854 \)
Calculation of HCF (H)
Solving for \( H \):
\( H = \frac{854}{61} = 14 \)
Calculation of LCM (L)
Now, we calculate \( L \) using the relation \( L = 60H \):
\( L = 60 \times 14 = 840 \)
Identification of the Other Number
Let the two numbers be \( a = 70 \) and \( b \). The relationship between the LCM and HCF of two numbers is:
\( a \times b = L \times H \)
Therefore, we have \( 70 \times b = 840 \times 14 \)
Solving for \( b \):
\( 70b = 11760 \)
\( b = \frac{11760}{70} \)
\( b = 168 \)
Consequently, the other number is 168.