Problem Analysis:

• We are given the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers.
• We are also given one of the numbers.
• The goal is to find the second number.
• Key terms: HCF, LCM, two numbers, find the other number.

Fundamental Number Property

There's a key relationship between two numbers and their HCF and LCM:

The product of two numbers is equal to the product of their HCF and LCM.

Mathematically, for two numbers $a$ and $b$: $a \times b = \text{HCF}(a, b) \times \text{LCM}(a, b)$

Identifying Given Values

Let the two numbers be $a$ and $b$. From the question:

• HCF = 17
• LCM = 1224
• Let $a = 136$
• We need to find $b$.

Calculating the Other Number

Using the property $a \times b = \text{HCF} \times \text{LCM}$:
$136 \times b = 17 \times 1224$

To find $b$, we rearrange the equation:

Now, we simplify the calculation:

1. Notice that $136$ is divisible by $17$. Specifically, $136 = 17 \times 8$.
2. Substitute this into the equation: $b = \frac{17 \times 1224}{17 \times 8}$
3. Cancel out the common factor $17$: $b = \frac{1224}{8}$
4. Perform the division: $b = 153$

Therefore, the other number is 153.