Question

Find LCM of $ 10,20,25 $ by long division method.
(A) $ 10 $
(B) $ 20 $
(C) $ 25 $
(D) $ 100 $

Answer 1

Hint: In this problem to find LCM of given numbers, first we will write the numbers in a single row. Then, we will divide by the least suitable prime number which divides at least one of the given numbers. We will continue this process until we get all coprime numbers in the last row. Then, the product of all the prime numbers will give LCM of given numbers.

Complete step-by-step answer:
In this problem, we have three numbers $ 10,20,25 $ and we have to find LCM of these numbers by using a long division method. For this, we will apply the following steps:
 $ \left( 1 \right) $ First we will write the given numbers in a single row.
 $ \left( 2 \right) $ We will divide by the least suitable prime number which divides at least one of the given numbers. Here, it will be $ 2 $ because $ 10,20 $ are even numbers. The number $ 25 $ is not divisible by $ 2 $ so it will be written as such in the next row.
 $ \left( 3 \right) $ Continue the procedure of step $ \left( 2 \right) $ . That is, again divide by $ 2 $ . The numbers which are not divisible by $ 2 $ will be written as such in the next row.
 $ \left( 4 \right) $ Now divide by $ 5 $ . The numbers which are not divisible by $ 5 $ will be written as such in the next row.
 $ \left( 5 \right) $ Continue this procedure until we get all coprime numbers in the last row.
 $ \left( 6 \right) $ The product of all the prime numbers (of the first column) will give LCM of given numbers.

$ 2 $	$ 10 $	$ 20 $	$ 25 $
$ 2 $	$ 5 $	$ 10 $	$ 25 $
$ 5 $	$ 5 $	$ 5 $	$ 25 $
$ 5 $	$ 1 $	$ 1 $	$ 5 $
	$ 1 $	$ 1 $	$ 1 $

Hence, the LCM of $ 10,20,25 $ is $ 2 \times 2 \times 5 \times 5 = 100 $ . Hence, option D is correct.
So, the correct answer is “Option D”.

Note: The lowest (least) common multiple of two or more given numbers is the smallest of their common multiples. If the number is even then it is divisible by $ 2 $ . If the unit digit of the number is $ 0 $ or $ 5 $ then that number is divisible by $ 5 $ . Remember that we can find LCM of the given numbers by long division method as well as by prime factorization method.