Question

What is the least common multiple of 5 and 7?

Answer 1

Hint: We need to find out the least common multiple of 5 and 7. We start to solve the problem by writing the multiples of the numbers 5 and 7. Then, we find the smallest common multiple of both the numbers.

Complete step by step solution:
We need to find the least common multiple of the numbers 5 and 7. We will be solving the given question by writing the multiples of both the numbers and then finding out the smallest common multiple of the numbers.
A multiple is a number that can be divided by another number several times without any remainder.
For example,
First five multiples of 8: 8, 16, 24, 32, 40
Reason : The product of each of the pairs (8,1) ,(8,2),(8,3),(8,4),(8,5) results in 8 , 16 , 24 , 32 , 40 respectively . Hence 8 , 16 , 24 , 32 , 40 are multiples of 8.
According to our question,
We need to find out the multiples of 5 and 7.
Writing the first seven multiples of 5,
$\Rightarrow 5\times 1=5$
$\Rightarrow 5\times 2=10$
$\Rightarrow 5\times 3=15$
$\Rightarrow 5\times 4=20$
$\Rightarrow 5\times 5=25$
$\Rightarrow 5\times 6=30$
$\Rightarrow 5\times 7=35$
The first seven multiples of 5: 5, 10, 15, 20, 25, 30, 35
Writing the first seven multiples of 7,
$\Rightarrow 7\times 1=7$
$\Rightarrow 7\times 2=14$
$\Rightarrow 7\times 3=21$
$\Rightarrow 7\times 4=28$
$\Rightarrow 7\times 5=35$
$\Rightarrow 7\times 6=42$
$\Rightarrow 7\times 7=49$
The first seven multiples of 7: 7, 14, 21, 28, 35, 42, 49
Now,
We have to find the least common multiple of 5 and 7.
From the above, we find that there is no number lesser than 35 that is a multiple of both 5 and 7. So, 35 is the smallest common multiple of 5 and 7.

$\therefore$ The least common multiple of 5 and 7 is 35.

Note: The result of the given question is correct if it divides both 5 and 7 exactly with no remainder. In our question, we got the result of 35.
$\Rightarrow 5\times 7=35$
$\Rightarrow 7\times 5=35$
The number 35 divides 5 and 7 exactly with no remainder. The result attained is correct. The multiple is the result we get upon the multiplication of a number with the whole number.