Question

What is the least common multiple of \[15\] and \[60\] ?

Answer 1

Hint: Least Common Multiple or LCM is the smallest positive number that is a common multiple of two or more numbers .There are multiple ways to find LCM -Calculating multiples and finding the smallest common multiple , Calculating from Prime factors , Division method or ladder method .

Complete step by step solution:
Multiple:
When we multiply a number by another number the result we get is called multiple of the first number .
Common Multiple :
Common multiples are the multiples of two or more numbers which are the same .
Example : \[20\] is multiple of \[4\] as well as \[5\] .
To know the least common multiple of two numbers we need to find the multiple of both the numbers first . Then we need to find which smallest multiple is common for both the numbers .
Here we need to find the least common multiple or LCM of \[15\] and \[60\] .
So first we need to find the multiples of the number \[15\] and we need to find the multiples of the number \[60\] . Then we need to find the smallest common multiple .
Multiples of 15 are :
\[15\] , \[30\] , \[45\] , \[60\] , \[75\] , \[90\] , \[105\] , \[120\] , \[135\] , \[150\] , \[165\] , \[180\] etc
Multiples of \[60\] are :
\[60\] , \[120\] , \[180\] , \[240\] etc
Here we can see that all the multiples of \[60\] are also the multiples of \[15\] also .
We need the least common multiple .
The smallest common multiple of \[15\] and \[60\] is \[60\] .
So the least common multiple of \[15\] and \[60\] is \[60\] .
This is our answer .
So, the correct answer is “60”.

Note: Whatever method we follow we will get the same answer . Depending upon the numbers of which we need to find LCM we should choose a method , as some methods are quick for a particular bunch of numbers .For few numbers this method will give desired value for more numbers other methods are useful.