If a number is divisible by both 3 and 4, which of the following must also be true?
Practice Questions
1 question
Q1
If a number is divisible by both 3 and 4, which of the following must also be true?
It is divisible by 12.
It is divisible by 7.
It is divisible by 6.
It is divisible by 9.
The least common multiple of 3 and 4 is 12, so any number divisible by both must also be divisible by 12.
Questions & Step-by-step Solutions
1 item
Q
Q: If a number is divisible by both 3 and 4, which of the following must also be true?
Solution: The least common multiple of 3 and 4 is 12, so any number divisible by both must also be divisible by 12.
Steps: 5
Step 1: Understand what it means for a number to be divisible by another number. A number is divisible by another if you can divide it by that number without leaving a remainder.
Step 2: Identify the numbers we are working with, which are 3 and 4.
Step 3: Find the least common multiple (LCM) of 3 and 4. The LCM is the smallest number that both 3 and 4 can divide into evenly.
Step 4: Calculate the LCM of 3 and 4. The multiples of 3 are 3, 6, 9, 12, 15, ... and the multiples of 4 are 4, 8, 12, 16, ... The smallest number that appears in both lists is 12.
Step 5: Conclude that if a number is divisible by both 3 and 4, it must also be divisible by their LCM, which is 12.
