Question

Find the smallest number divisible by numbers 2 to 9 (both inclusive).

Answer 1

Hint:
LCM is elaborated as Least Common Multiple, which is the lowest common factor among the integers. To find the LCM of the given numbers, which is divisible by all numbers for which we are finding the LCM, the method includes basic factorization of the numbers to find factors that are multiplied together to form a number. If the all given numbers are \[0\]for which LCM is being calculated, their LCM will also be \[0\]. First, find the factors of the number that are the number when multiplied together gives the original number.

Complete step by step solution:
To find the lowest common multiple of the numbers, let’s find the factors of the given numbers for which we have to find the LCM of each number.
Factors are the integers, which, when multiplied, results in the original number only. First, find the factors of numbers \[2,3,4,5,6,7,8,9\]
\[
  2 = 2 \times 1 \\
  3 = 3 \times 1 \\
  4 = 2 \times 2 \times 1 \\
  5 = 5 \times 1 \\
  6 = 3 \times 2 \times 1 \\
  7 = 7 \times 1 \\
  8 = 2 \times 2 \times 2 \times 1 \\
  9 = 3 \times 3 \times 1 \\
 \]
The unique (single) common multiple between all the numbers ranging from 2 to 9 is \[7 \times 5 \times 3 \times 3 \times 2 \times 2 \times 2 \times 1\]
Hence, the LCM of the numbers \[2,3,4,5,6,7,8,9\] is:
\[7 \times 5 \times 3 \times 3 \times 2 \times 2 \times 2 \times 1 = 2520\]
Hence, \[2520\] is the number which is completely divided by any number between 2 to 9.

Note:
Each and every unique integer in the factors of the numbers will contribute towards the least common multiple of a group of a number. In general, LCM is the common multiple of the numbers, which will divide all the numbers participating in the solution completely without leaving any remainder.