Fing two pairs of numbers with the given number as their least common multiple?

Question

Its obout Least Common Multiple

Answer 1

First, what is a multiple? It is like adding a number to itself any number of times. For example, every number is a multiple of one. 1 times anything is that number. Multiples of 2 are all the even numbers. So multiples are like counting, but instead of counting by one, you count by whatever number you're finding multiples for.

A least common multiple is something that two numbers share. You find it by making a set of all the multiples for each number. The least common multiple is the lowest number you find in BOTH sets of multiples.

To find two pairs of numbers that share a given least common multiple, list the products and their sets of multiples.

Let's say the given number is 12...

List its factors

1,2,3,4,6,12...

now consider the multiples of each number.

2,4,6,8,10,12
3,6,9,12
4,8,12
6,12

Okay so 3 and 4 have a LCM of 12.
Also 4 and 6 do. 3 and 6 have a least common multiple of 6, and 2 has LCMs of 4 or 6, depending on which other number it's with. So only 3,4 and 4,6 work:)