Question

What is the smallest positive integer divisible by 6 and 2 that you can write using at least one 2 and one 6? Please use the digits 2 and 6 only. a) 6 b) 12 c) 26 d) 62

Answer 1

The smallest positive integer divisible by 6 and 2 that can be made using the digits 2 and 6 is 12, which satisfies both divisibility requirements and uses the digits 2 and 6.

Step-by-step explanation:

The smallest positive integer divisible by both 6 and 2, and composed exclusively of the digits 2 and 6 is 12. This number satisfies the divisibility requirements: it can be divided evenly by both 6 (2 times) and 2 (6 times). To find the least common multiple (LCM) of 6 and 2, which is 6, we note that any multiple of 6 is automatically divisible by 2 since 6 itself contains the factor 2. Therefore, the smallest number we can make with at least one 2 and one 6 that is divisible by 6 and 2 is 12. Option b, 12, is the correct answer.

Answer 2

The smallest positive integer divisible by 6 and 2 that uses the digits 2 and 6 is option b, 12. This satisfies the conditions of being divisible by both numbers and using the given digits.

Step-by-step explanation:

The smallest positive integer divisible by both 6 and 2, that can be written using at least one 2 and one 6, from the given options is 26. However, 26 is not divisible by 6, and so it does not meet the criteria of the question. Therefore, we must look at the other options provided. Option b, 12, is divisible by 6 and 2, and uses the digits 2 and 6. This makes 12 the smallest positive integer that satisfies all the given conditions. Option a, 6, does not include a 2, and options c (26) and d (62) are not divisible by 6. The correct answer is b, 12.

To confirm, we can check the divisibility:

• 6 divides into 12: 12 ÷ 6 = 2.
• 2 divides into 12: 12 ÷ 2 = 6.

And since 12 is made up of the digits 2 and 6, it fulfills all parts of the question.