This problem requires us to find a number from the given options that is divisible by both 37 and 8. We can determine this by checking the divisibility rules for both numbers.

Checking Divisibility by 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. Let's examine the last three digits of each option:

• 15370: The last three digits form 370.
• 14208: The last three digits form 208.
• 13702: The last three digits form 702.
• 15659: The last three digits form 659.

Checking Divisibility by 37

There is no simple shortcut rule for divisibility by 37. We typically check this by performing the division. Alternatively, since 37 and 8 are coprime (meaning they share no common factors other than 1), any number divisible by both must also be divisible by their least common multiple (LCM), which is their product: $37 \times 8 = 296$.

Analyzing the Options

We will test each number for divisibility by 8 and then by 37 (or by 296).

Number Divisibility Using LCM

As mentioned earlier, a number divisible by both 37 and 8 must be divisible by their LCM, which is 296.

Let's check the division by 296 for each option:

• $15370 \div 296 \approx 51.92$ (Not divisible)
• $14208 \div 296 = 48$ (Divisible)
• $13702 \div 296 \approx 46.29$ (Not divisible)
• $15659 \div 296 \approx 52.89$ (Not divisible)

This method also confirms that 14208 is the only number divisible by 296.

Final Answer Determination

Based on the divisibility checks, the number 14208 is divisible by 8 (since 208 is divisible by 8) and also divisible by 37 (as $14208 / 37 = 384$). Therefore, 14208 satisfies the condition of being divisible by both 37 and 8.