Question

A number is divisible by 3 and 5. What is the smallest such number greater than 100? 
 

• A. 105
• B. 120
• C. 135
• D. 150

Hint:

For “divisible by both” problems, find the LCM and choose the required multiple.

Answer 1

The Correct Option is A

To find the smallest number greater than 100 that is divisible by both 3 and 5, we start by noting that a number is divisible by both 3 and 5 if and only if it is divisible by their least common multiple (LCM). The LCM of 3 and 5 is calculated as follows:

Step 1: List the prime factors of 3 and 5. Since both are prime numbers, the factors are:

• 3: 3
• 5: 5

Step 2: Calculate the LCM.

The LCM is found by taking the highest power of each prime factor appearing in the factorizations. Here, LCM(3, 5) = 3 x 5 = 15.

Step 3: Find the smallest number greater than 100 that is divisible by 15. We calculate:

100 ÷ 15 = 6 remainder 10, which means the next multiple of 15 is 15 x 7 = 105.

Conclusion: 105 is the smallest number greater than 100 that is divisible by both 3 and 5.