Question

two numbers have these properties both numbers are greater than 8 their highest common factor is 8 their lowest common multiple is 80 find the two numbers

Answer 1

Answer: 8 and 80

Step-by-step explanation:

8 * 5 = 40

8 * 10 = 80

8 must be the hcf of two separate numbers. So, one of them must be 8, and the other must be greater than 8.

Multiples of 8:

8

16

24

32

40

48

56

64

72

80

The numbers on that list that multiply evenly to 80:

8, 16, 40, 80

16 is the lowest common multiple of 16 and 8

40 is the lowest common multiple of 40 and 8

80 is the lowest common multiple of 80 and 8

So the two numbers are 8 and 80; the highest common factor (HCF) is indeed 8.

Answer 2

The required two numbers that are greater than 8 are 10 and 16.

What is HCF?

The Highest Common Factor (HCF) is the greatest number among all common factors of two or more numbers. For example, the HCF of 14 and 8 is 2.

What is LCM?

The Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers in a group. For example, the LCM of 14 and 8 is 56.

Formula:

Let x and y be two numbers. Then we can write

HCF of x and y × LCM of x and y = x×y

How to solve this problem?

Given that HCF and LCM of the required numbers are 8 and 80 respectively. We have to find two numbers that are greater than 8. Let us assume that a and b be the required numbers.

Using above formula,

a×b = 8×80

i.e. ab = 8×2×40 = 16×40

Clearly, the HCF and LCM of 16 and 40 are 8 and 80 respectively. They are also greater than 8.

So, the required two numbers that are greater than 8 are 10 and 16.

Know more about HCF and LCM here -

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