If a number is divisible by both 2 and 3, which of the following is true?
Practice Questions
1 question
Q1
If a number is divisible by both 2 and 3, which of the following is true?
It is divisible by 5
It is divisible by 6
It is odd
It is a prime number
A number that is divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Questions & Step-by-step Solutions
1 item
Q
Q: If a number is divisible by both 2 and 3, which of the following is true?
Solution: A number that is divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Steps: 5
Step 1: Understand what it means for a number to be divisible by 2. A number is divisible by 2 if it is even, meaning it ends in 0, 2, 4, 6, or 8.
Step 2: Understand what it means for a number to be divisible by 3. A number is divisible by 3 if the sum of its digits is divisible by 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 without leaving a remainder.
Step 4: Calculate the LCM of 2 and 3. The multiples of 2 are 2, 4, 6, 8, 10, ... and the multiples of 3 are 3, 6, 9, 12, ... The smallest number that appears in both lists is 6.
Step 5: Conclude that if a number is divisible by both 2 and 3, it must also be divisible by 6, since 6 is the LCM of 2 and 3.
