Divisibility Check Strategy

To find a number divisible by both 17 and 13, we need to find a number divisible by their least common multiple (LCM).

Since 17 and 13 are prime numbers, their LCM is their product:

$ \text{LCM}(17, 13) = 17 \times 13 = 221 $

Therefore, the required number must be divisible by 221.

Testing Divisibility

We will now check the divisibility of each option by 221:

• Option 1: $22372 \div 221 \approx 101.23$ (Not divisible)
• Option 2: $21401 \div 221 \approx 96.83$ (Not divisible)
• Option 3: $21658 \div 221 = 98$ (Divisible)
• Option 4: $20049 \div 221 \approx 90.72$ (Not divisible)

Conclusion

The number 21658 is the only option divisible by 221, meaning it is divisible by both 17 and 13.