Question

How do you find the LCM of \[35,25\] ?

Answer 1

Hint: In order to find the LCM of the numbers write the prime factors of the given numbers, find the least common multiple which is suitable for both the numbers. The number obtained must be the multiple of both the numbers \[35,25\] then only it will be called as their LCM.

Complete step by step solution:
We are given \[35,25\] to find their LCM, but first we should know what is LCM.
LCM stands for Least common multiple. A number which is the multiple of all the numbers listed to find the LCM.
The prime factors of the given numbers are:
 \[35 = 5 \times 7\]
 \[25 = 5 \times 5\]
We can see that the least number which is a multiple of \[25\] is \[5 \times 5\] , i.e two \[5's\] .
Similarly, for \[35\] , the least number that is its multiple is \[5 \times 7\] , i.e one \[5\] and one \[7\] .
In order to find the LCM of both the numbers \[35\] and \[25\] , we need to find the multiple by combining the factors obtained above.
For \[25\] we need two \[5's\] , i.e \[5 \times 5\] and for \[35\] we need one \[7\] and one \[5\] that can be taken from the two \[5's\] of \[25\] as we are finding together.
So, the multiple becomes:
 \[35,25 = 5 \times 5 \times 7 = 175\] which included two \[5's\] of \[25\] and one \[5\] and one \[7\] for \[35\] .
Therefore, the Least Common Multiple (LCM) is \[175\].

Note: Do not include three \[5's\] and one \[7\] for the LCM, otherwise it would not give the correct answer.
We can also solve for LCM by simply listing some of the multiples of \[35,25\] then the first common multiple of both the numbers becomes the LCM.
For example, the multiple of the numbers are:
 \[25 = 25,50,75,100,125,150,175,200,225.....\]
 \[35 = 35,70,105,140,175,210,245....\]
We can see that the first common value obtained is \[175\] , and this is our LCM for both the numbers.