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?
  1. It is divisible by 5.
  2. It is divisible by 6.
  3. It is an odd number.
  4. 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.
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