Question

The HCF of two numbers is 20. The LCM of both numbers is a multiple of 14. One number is greater than the other, work out the smallest possible values of both numbers.

Answer 1

The smallest combination of the numbers is 20 and 140

Explanation:

The given parameters are;

The Highest Common Factor HCF of the two number = 20

The Lowest Common Multiple LCM of both numbers = Multiple of 14

Let x and y represent the two numbers, we are given;

x > y

We have;

`L.C.M. = (Product \ of \ the \ numbers)/(H.C.F.)`

Substituting the known values, we have;

`x * 14 = (Product \ of \ the \ numbers)/(20)`

The product of the numbers = x × 14 × 20

The possible products of the numbers are;

280, 560, 840, 1,120, 1,400, 1,680, 1,960, 2,240, 2.520, 2,800, 3,080, 3,360, 3,640, 3,920

Dividing the possible products by 20 gives, the smallest quotient that is also a multiple of 20 as 140, from which we have;

20 × 140 = 2,800

Therefore, the smallest combination of the numbers = 20 and 140.