Question

Two numbers have these properties.

Both numbers are greater than 8.
Their highest common factor (HCF) is 8.
Their lowest common multiple (LCM) is 80.
Find the two numbers, writing your answers on one line in the form,
The two numbers are ... and ...​

Answer 1

• 16 and 40

Explanation:

Let the numbers be x and y

HCF is 8, so both numbers are multiples of 8 ⇒ x = 8n, y = 8m

As per property of numbers, the product of numbers is equal to product of their LCM and HCF:

• xy = HCF(x,y) × LCM(x,y)

Since LCM(x,y) = 80 we have:

• 8×80 = xy
• 8×80 = 8n×8m
• 10 = nm

Possible option:

• n = 2, m = 5

Then the numbers are:

• x = 2*8= 16
• y = 5*8 = 40