Question: If a number is divisible by both 2 and 3, which of the following must also be true?
Options:
It is divisible by 5.
It is divisible by 6.
It is an odd number.
It is a prime number.
Correct Answer: It is divisible by 6.
Solution:
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
If a number is divisible by both 2 and 3, which of the following must also be tr
Practice Questions
Q1
If a number is divisible by both 2 and 3, which of the following must also be true?
It is divisible by 5.
It is divisible by 6.
It is an odd number.
It is a prime number.
Questions & Step-by-Step Solutions
If a number is divisible by both 2 and 3, which of the following must also be true?
Step 1: Understand what it means for a number to be divisible by 2. A number is divisible by 2 if it can be divided by 2 without leaving a remainder.
Step 2: Understand what it means for a number to be divisible by 3. A number is divisible by 3 if it can be divided by 3 without leaving a remainder.
Step 3: If a number is divisible by both 2 and 3, it means it can be divided by both 2 and 3 without any remainder.
Step 4: 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 5: Calculate the LCM of 2 and 3. The LCM of 2 and 3 is 6.
Step 6: 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.
Divisibility Rules – Understanding the rules of divisibility for numbers, particularly how to determine if a number is divisible by 2, 3, and their least common multiple.
Least Common Multiple (LCM) – The concept of finding the least common multiple of two numbers and its implications for divisibility.
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