The multiples of 6 less than 200 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, and 198.
There are a total of 33 multiples of 6 less than 200.
What are multiples?
A multiple of a number is the result of multiplying that number by an integer. Multiples are essentially the numbers in a number's multiplication table. For example, the multiples of 6 are 6, 12, 18, 24, and so on, which are derived from 6×16 cross 1
6×1
, 6×26 cross 2
6×2
, 6×36 cross 3
6×3
, etc. The list of multiples is infinite, but in this case, it is limited to those less than 200.
How to find the multiples of 6 less than 200
Multiples of 6 less than 200 can be found by repeatedly adding 6 starting from 6, or by multiplying 6 by consecutive whole numbers starting from 1. To find the last multiple under 200 and the total number of multiples, divide 200 by 6. The result is 33 with a remainder of 2. This means that 6×33=1986 cross 33 equals 198
6×33=198
is the largest multiple of 6 less than 200, and there are 33 such multiples. This can also be confirmed by formulating an arithmetic sequence.
Properties and patterns of multiples of 6
Multiples of 6 are characterized by several properties:
- A number is a multiple of 6 if and only if it is divisible by both 2 and 3. This implies the number must be even and the sum of its digits must be a multiple of 3.
- All multiples of 6 are even numbers.
- The unit digits of multiples of 6 follow a repeating pattern: 6, 2, 8, 4, 0.
Real-world applications
The concept of multiples of 6 has practical applications in various areas:
- Timekeeping: Units of time like minutes and seconds (60) are multiples of 6, useful for time calculations.
- Grouping: Multiples help determine how many groups of 6 can be formed from a given quantity.
- Mathematical problems: Understanding multiples is essential for solving problems involving the least common multiple (LCM) and greatest common divisor (GCD).