Question

What is the LCM of 7 and 10?

Answer 1

Hint: LCM denotes the Least Common Multiple. It is also called the Least Common Divisor (LCD). We are going to use three different methods to solve it, the first method is simply based on the definition of LCM, which is LCM of two numbers is the smallest whole number which is a multiple of both. Whereby multiple we mean that a number that can be divided by another number a certain number of times without a remainder.

Complete step by step solution:
So, let’s start with the first method,
Write down few multiples of 7
\[7\text{ 14 21 28 35 42 49 56 63 70}\]
And a few multiples of 10
\[10\text{ 20 30 40 50 60 70}\]
Note that, the lowest number we have in common is 70 so LCM of 7 and 10 is 70.
Let’s have a look at the second method
We have a direct formula to find the LCM, for that we define another term called GCF (greatest common factor)
So, the formula is
\[LCM\left( a,b \right)=\dfrac{\left( a\times b \right)}{GCF}\]
We can easily see that there is no common factor in 7 and 10 others than 1.
So
\[GCF\left( a,b \right)=1\]
So, by the above formula
\[\begin{align}
  & LCM\left( 7.10 \right)=\dfrac{\left( 7\times 10 \right)}{1} \\
 & LCM\left( 7,10 \right)=70 \\
\end{align}\]
The last method is to use the common division method, it is pretty same as our first method
\[\begin{align}
  & 7\left| \!{\underline {\,
  \text{7 , 10} \,}} \right. \\
 & 2\left| \!{\underline {\,
  1\text{ ,10} \,}} \right. \text{ } \\
 & 5\left| \!{\underline {\,
  1\text{ , 5} \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1\text{ , }1 \,}} \right. \\
\end{align}\]
Now, computing it we get
\[\begin{align}
  & LCM=7\times 5\times 2 \\
 & LCM=70 \\
\end{align}\]
By all the three methods we can say that LCM of 7 and 10 is 70.

Note: You can remember a point while solving a question related to LCM and HCF that LCM can never be less than any of the given numbers. That is LCM is always either less than or equal to any one of the given numbers. In simple words the lowest possible of LCM is anyone given the numbers itself. Similarly, for HCF it is just the opposite, it is always less than or equal to any one of the given numbers.