Kenny is thinking of two numbers greater than 10. "The highest common factor (HCF) of my two numbers is 7
The lowest common multiple (LCM) of my two numbers is 84”
He says:
Write down the two numbers that Kenny is thinking of.

Highest common factor is the greatest factor between two or more number. Least common factor least number which is divisible by two numbers.The two numbers that Kenny is thinking of are 21 and 24.

The least common factor (HCF) of the two numbers is 7.

The highest common factor  (LCM) of the two numbers is 84.

The two number are greater than 10.

Highest common factor is the greatest factor between two or more number.

Least common factor least number which is divisible by two numbers.

As the number is LCM is 7, thus the number must be the multiple of 7. Both the number are greater than 10. Thus the possible number should be greater than 14(multiple of 7 and greater than 10) and less than 84 ( LCM is 84).

The possible number for the above condition are,

14,21,28,35,42,49,56,63,70,77 and 84.

Both the number must divide the number 84. In the above number only 14,21,28,42 and 84 can divide the number 84.

The product of both the number must be equal to the product of the HCF and LCM. The product of the HCF and LCM,

From the above possible points only the product of 21 and 24 is equal to the 504.

Thus the two numbers that Kenny is thinking of are 21 and 24.

Learn more about the highest common factor here;

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The numbers are 21 and 28

Step-by-step explanation:

Here, we want to write out the two numbers from the information in the question

Firstly, the two numbers are greater than 10

The highest common factor of both numbers is 7

While the lowest common multiple of both numbers is 84

Since 7 is a factor of both, the numbers must be multiples of 7

So let us list out the multiples of 7 greater than 10

14, 21 , 28 , 35 , 42 , 49, 56 , 63 , 70 , 77 , 84 ,

The numbers cannot be greater than 84

out of all, only the following is a multiple of 84;

14,21 , 28 , 42 and 84

The correct answers here are 21 and 28

Reason for this is that only the two satisfied the properties given

32

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