A pair of numbers has an HCF (Highest Common Factor) of 7 , and an LCM (Lowest Common Multiple) of 42 . What is the pair of numbers

14 and 21

Step-by-step explanation:

This is not an easy question, but luckily we can have an idea to solve this.

In this case, we need to apply the relation between HCF and LCM, which is the following:

HCM * LCM = Number 1 * Number 2

In other words, the multiplication of both factors is equal to the multiplication of the given numbers that we are looking for. Now, we do not know the numbers but we can have an idea of which numbers can be when we calculate the product of the factors:

HCM * LCM = 42 * 7 = 294

We know that the products should result 294, and if the HCM is 7, means that both numbers can be divided by 7 as the highest factor, so, let's write the multiple of 7:

Multiples of 7:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70

With these we can have an idea, if 42 * 7 = 294, all we just need is to find others two numbers that the result gives 294:

14 * 7 = 98

14 * 21 = 294

14 and 21 could be the numbers, but let's confirm writting their multiples

HCM of 14: 1, 2, 7, 14

HCM of 21: 1, 3, 7, 21

LCM of 14: 14, 28, 42, 56, 70

LCM of 21: 21, 42, 63, 84

As you can see, The HCM and LCM of 14 and 21 are 7 and 42, therefore the pair of numbers are:

Hope this helps