 # 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

## 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.

### Video Lesson on Common Multiples ## 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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## Frequently Asked Questions – FAQs

### What are the first ten multiples of 7 in Maths?

The first ten multiples of 7 in Maths are 7, 14, 21, 28, 35, 42, 49, 56, 63 and 70.

### What are the multiples of 7 between 1 to 100?

The multiples of 7 between 1 to 100 are 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 , 70, 77, 84, 91, 98.

### How many multiples of 7 fall between 40 and 60?

Between 40 and 60, there are only three multiples of 7, they are 42, 49 and 56.

### What are the multiples of 7 between 100 to 200?

The multiples of 7 between 100 to 200 are 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, and 196.

### How many multiples does 7 have?

The number 7 can have infinitely many multiples.

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