If a number is divisible by both 8 and 12, which of the following must also be t
Practice Questions
Q1
If a number is divisible by both 8 and 12, which of the following must also be true?
It is divisible by 24.
It is divisible by 16.
It is divisible by 20.
It is divisible by 32.
Questions & Step-by-Step Solutions
If a number is divisible by both 8 and 12, which of the following must also be true?
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 numbers we are working with: 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: To find the LCM of 8 and 12, list the multiples of each number: Multiples of 8 are 8, 16, 24, 32, ... and multiples of 12 are 12, 24, 36, ...
Step 5: Look for the smallest number that appears in both lists of multiples. The smallest number is 24.
Step 6: Conclude that if a number is divisible by both 8 and 12, it must also be divisible by their LCM, which is 24.
Divisibility – Understanding the conditions under which a number can be divided by another without leaving a remainder.
Least Common Multiple (LCM) – The smallest multiple that is exactly divisible by two or more numbers.
