L.C.M. H.C.F. and Numbers Relationship

This problem involves finding a missing number given its L.C.M., H.C.F., and one of the numbers. We use the fundamental relationship between these values.

Given:

• L.C.M. = 156
• H.C.F. = 13
• One number (let's call it $a$) = 78
• The other number (let's call it $b$) is unknown.

Formula: Product of Numbers equals L.C.M. times H.C.F.

The core principle is that the product of two numbers ($a$ and $b$) is equivalent to the product of their L.C.M. and H.C.F.

Mathematically: $a \times b = \text{L.C.M.} \times \text{H.C.F.}$

Unknown Number Calculation

1. Plug the given values into the formula: $78 \times b = 156 \times 13$
2. Isolate $b$ to solve for the unknown number: $b = \frac{156 \times 13}{78}$
3. Perform the calculation:

   Simplify the fraction. Notice $156 = 2 \times 78$.

   $b = \frac{(2 \times 78) \times 13}{78}$

   Cancel out the 78:

   $b = 2 \times 13$ $b = 26$

The other number is 26.