Multiples of 7
Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, … and so on. How do we get to know a number is multiple of another number? If a number is multiple of another number, then it is evenly divisible by the original number. For example, 14 divided by 7 is equal to 2, thus it is a multiple of 7.
Any number that can be denoted in the form 7n where n is a natural number is a multiple of 7. So if two values p and q are there, we say that q is a multiple of p if q = np for some natural number n. Let’s look at the factors and multiples of 7 here.
| 7 | 14 | 70 | 700 | 77 |
All numbers which can be divided by 7 are a multiple of 7. For example, 7, 70, 77 and 49 are all multiples of 7 for the following reasons
| 49 | = | 7 | x | 7 |
| 70 | = | 7 | x | 10 |
| 7 | = | 7 | x | 1 |
| 77 | = | 7 | x | 11 |
These values are called as multiples because these values are obtained by adding or subtracting original value many times.
What is Multiple?
A multiple is a numerical value that is generated when a natural number is multiplied by another natural number or counting number.
Multiples of 7 can be generated by multiplying 7 to the counting numbers. Let us see the list og multiples of number 7 in the next section.
List of Multiples of 7
| Multiplication | Multiples of 7 |
| 7 x 1 | 7 |
| 7 x 7 | 14 |
| 7 x 3 | 21 |
| 7 x 4 | 28 |
| 7 x 5 | 35 |
| 7 x 6 | 42 |
| 7 x 7 | 49 |
| 7 x 8 | 56 |
| 7 x 9 | 63 |
| 7 x 10 | 70 |
| 7 x 11 | 77 |
| 7 x 12 | 84 |
| 7 x 13 | 91 |
| 7 x 14 | 98 |
| 7 x 15 | 105 |
| 7 x 16 | 112 |
| 7 x 17 | 119 |
| 7 x 18 | 126 |
| 7 x 19 | 133 |
| 7 x 20 | 140 |
Check Other Multiples
What is Common Multiple?
Common multiple is a whole number that is common to two or more numbers. It means two or more numbers share a single whole number as a common multiple. Let us understand with the help of examples.
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,..
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,…
We can see the common multiple of 4 and 7, from the above-given multiples is 28. Therefore, 28 is the least common multiple of 4 and 7.
Solved Examples
Q.1: What is the sum of the first five multiples of 7?
Answer: The first five multiples of seven are 7, 14, 21, 28 and 35
Sum = 7 + 14 + 21 + 28 + 35 = 105
Q.2: What is the average of the first ten multiples of 7?
Answer: The average of the first ten multiples of 7 is equal to the sum of all the multiples divided by 10.
Average = (7+14+21+28+35+42+49+56+63+70)/10
= 385/10
= 38.5
Therefore, the required average is 38.5.
Q.3: How to check if a number is a multiple of 7?
Answer: If a number is multiple of 7, then it is evenly divisible by 7.
Suppose, 49 is a multiple of 7 because 49/7 = 7
Let us check if 66 is the multiple of 7 or not.
66/7 = 9.42.. (Quotient is a fraction)
Therefore, 66 is not a multiple.
Q.4: What are the multiples of 7 that are less than 30?
Answer: The multiples of natural number 7, which are less than 30 are 7,14,21 and 28.
Q.5: What is the least common multiple of 6 and 7?
Answer: To find the least common multiple of 6 and 7, first we will write the multiples of each of the numbers.
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
Therefore, we can see, the LCM of 6 and 7 is 42.
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