Question

How do you find the least common multiple of \[10,{\text{ }}2{\text{ }}and{\text{ }}15.\]?

Answer 1

Hint: Here we are given with three numbers. We have to find the least common multiple of them. For that we will first find their multiples and then we will decide the least common multiple of them. Finding multiple is nothing but writing the table of that number. Here 15 is the biggest number among the three numbers given. We will start with it. So that it will be easy for us. Also we can use the prime factor method to find the LCM.

Complete step by step solution:
Now we have three numbers given \[10,{\text{ }}2{\text{ }}and{\text{ }}15.513\]
First we will find the multiples of \[15\].
Multiples of \[15\] are \[15,{\text{ }}30,{\text{ }}45,{\text{ }}60\]…and so on
Now multiples of \[10\] are \[10,{\text{ }}20,{\text{ }}30,{\text{ }}40\]…and so on
Here we can see that \[30\] is the least common multiple in \[15{\text{ }} and {\text{ }}10.\]
Now we just need to check whether it is a multiple of \[2\]also or not. So we know that if we multiply
\[2\] by \[15\] we get \[30\] as their product. So it is a multiple of \[2\].
This clears that \[30\] is the least common multiple of \[2,{\text{ }}10{\text{ }}and{\text{ }}15\].

Note: Note that multiples and factors are two different concepts. These three numbers do not have any common factor. To find LCM we also can use the prime factor method.
In this method we will use prime numbers only to find the LCM. The numbers are divided by prime numbers. Then the product of numbers in the left most column will give the LCM.

	\[15\]	\[10\]	\[2\]
\[2\]	\[15\]	\[5\]	\[1\]
\[3\]	\[5\]	\[5\]	\[1\]
\[5\]	\[1\]	\[1\]	\[1\]

LCM = \[2 \times 5 \times 3 = 30\]