If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
Practice Questions
1 question
Q1
If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
16
24
20
36
The least common multiple of 8 and 12 is 24, so the number must be divisible by 24.
Questions & Step-by-step Solutions
1 item
Q
Q: If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
Solution: The least common multiple of 8 and 12 is 24, so the number must be divisible by 24.
Steps: 7
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 them without leaving a remainder.
Step 2: Identify the two numbers we are considering: 8 and 12.
Step 3: Find the least common multiple (LCM) of 8 and 12. The LCM is the smallest number that both 8 and 12 can divide into without a remainder.
Step 4: List the multiples of 8: 8, 16, 24, 32, 40, ...
Step 5: List the multiples of 12: 12, 24, 36, 48, ...
Step 6: Find the smallest number that appears in both lists. The smallest number is 24.
Step 7: Conclude that if a number is divisible by both 8 and 12, it must also be divisible by their least common multiple, which is 24.
