Question: If a number is divisible by both 2 and 3, what is the smallest possible value?
Options:
2
3
6
12
Correct Answer: 6
Solution:
The least common multiple of 2 and 3 is 6.
If a number is divisible by both 2 and 3, what is the smallest possible value?
Practice Questions
Q1
If a number is divisible by both 2 and 3, what is the smallest possible value?
2
3
6
12
Questions & Step-by-Step Solutions
If a number is divisible by both 2 and 3, what is the smallest possible value?
Correct Answer: 6
Step 1: Understand what it means for a number to be divisible by another number. A number is divisible by 2 if it can be divided by 2 without leaving a remainder. Similarly, a number is divisible by 3 if it can be divided by 3 without leaving a remainder.
Step 2: Identify the numbers we are working with, which are 2 and 3.
Step 3: Find the least common multiple (LCM) of 2 and 3. The LCM is the smallest number that both 2 and 3 can divide into evenly.
Step 4: List the multiples of 2: 2, 4, 6, 8, 10, ...
Step 5: List the multiples of 3: 3, 6, 9, 12, ...
Step 6: Look for the smallest number that appears in both lists. The number 6 is the first number that appears in both lists.
Step 7: Conclude that the smallest number that is divisible by both 2 and 3 is 6.
Divisibility – Understanding the rules of divisibility for numbers, specifically for 2 and 3.
Least Common Multiple (LCM) – Calculating the least common multiple of two numbers to find a common multiple.
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