We are asked to find the least positive integer that is divisible by both 15 and 35.

Step 1: Find the Least Common Multiple (LCM)

The least positive integer that is divisible by both 15 and 35 is their Least Common Multiple (LCM).

1. Prime factorization of 15: $15 = 3 \times 5$

2. Prime factorization of 35: $35 = 5 \times 7$

Step 2: LCM Calculation

The LCM is the product of the highest powers of all prime factors that appear in any of the factorizations:

• From 15, we have the primes 3 and 5.
• From 35, we have the primes 5 and 7.

Now, take the highest powers of each prime:

• For 3: $3^1$,
• For 5: $5^1$,
• For 7: $7^1$.

The LCM is: $\text{LCM}(15, 35) = 3 \times 5 \times 7 = 105$

Conclusion:

The least positive integer divisible by both 15 and 35 is 105.

Thus, the correct answer is H. 105.

Would you like more details or have any other questions? Here are some related questions you might explore:

1. How do you calculate the Greatest Common Divisor (GCD) between two numbers?
2. What are the properties of LCM and GCD in number theory?
3. Can the LCM of three or more numbers be calculated similarly?
4. How do prime factorizations help in simplifying LCM calculations?
5. What are practical applications of finding the LCM in real-world problems?

Tip: When calculating the LCM, always remember to use the highest powers of each prime number in the factorization.