Question

Find the lowest number, which is more than 7 to be divided by 20, 50, and 100 exactly.

Answer 1

Hint: LCM or LCF is a method by which we can find out a common number. By using this common number, one can divide any number in the given set. In the above problem, we first find the LCM, and after adding number 7 to the result, will give us the required number.
Here, the question is not asking for the LCM directly but is asking the lowest number, which is more by 7, which will divide the numbers 20, 50, and 100 exactly without leaving any remainder behind. Hence, the question’s equation is reduced to $7 + x = LCM$, where $x$ is the desired result.

Complete Answer:
To determine the LCM, find the factors of \[20,50,100\]is:

The common factors among the numbers $20,50,100$ are $2 \times 2 \times 5 \times 5$.
Hence, \[LCM(100,50,20) = 2 \times 2 \times 5 \times 5 = 100\]
Now, let $x$ be the smallest integer, which when added to 7, will divide the numbers 20, 50, and 100 exactly.
Hence,
$
  100 = 7 + x \\
  x = 100 - 7 \\
  x = 93 \\
 $

Hence, $x = 93$ it is the smallest number that, when added with 7, will divide the numbers 10, 20, and 50 exactly.

Note: LCM of given numbers is exactly divisible by each of the numbers. During the LCM calculation, students must know the tables of various numbers, and they have to perform the operations step by step. Lastly, they have to multiply all the numbers by which they are dividing the given set of numbers. The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM (a, b), is the smallest positive integer that is divisible by both a and b.