If a number is divisible by both 2 and 3, we can conclude that it is also divisible by 6. This is because 6 is the least common multiple (LCM) of 2 and 3.
To understand this better, let’s break it down:
- Divisibility by 2: A number is divisible by 2 if it is an even number. This means that it ends in 0, 2, 4, 6, or 8.
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For example, the number 123 has a digit sum of 1 + 2 + 3 = 6, which is divisible by 3.
Since we are considering a number that meets both divisibility criteria, we can represent such a number mathematically:
If a number (let’s call it N) is divisible by 2, it can be expressed as:
N = 2k (where k is an integer)Similarly, if it is divisible by 3, it can be expressed as:
N = 3m (where m is another integer)To be divisible by both 2 and 3, N must satisfy the following condition:
N = 6n (where n is an integer)Thus, when a number can be divided both by 2 and 3 without leaving a remainder, it can also be divided evenly by 6. This conclusion allows us to categorize numbers effectively based on their divisibility.