Identify Common Factors, Common Multiples and Prime Numbers 5 - Reasoning

The task involves identifying pairs of numbers from a set of four—3, 8, 12, and 16—that share the same Lowest Common Multiple (LCM). The LCM is the smallest number that is a multiple of both numbers in the pair. Upon analysis, the pairs that have the same LCM are identified as (3 and 16) and (12 and 16), with their LCM being 48. Another pair identified is (3 and 8) and (8 and 12), which share an LCM of 24. The reasoning behind these findings lies in calculating the multiples of each number and determining the smallest common multiple shared by the pairs. For example, the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, and so on, while the multiples of 16 are 16, 32, 48, 64, and so on. The first common multiple they share is 48, hence the LCM for the pair (3 and 16) is 48. A similar approach is used to find the LCM for the other pairs.

It is important to note that the LCM is particularly useful when adding or subtracting fractions with different denominators, as it helps to find a common denominator. It is also used in solving problems that involve finding repeating patterns or combining frequencies. The exercise of determining the LCM of various pairs of numbers not only reinforces the concept of multiples but also enhances students' understanding of number relationships and their proficiency in the four operations of arithmetic: addition, subtraction, multiplication, and division.