Question

The HCF of two numbers is 6 and the product

Answer 1

Answer:

60

Step-by-step explanation:

There are two pairs of numbers whose product is 360, and their HCF is 6. They are 6 & 60, and 12 & 30.

Answer 2

Answer:

If the two numbers have a highest common factor of 6 , then we can write one number as 6∗a and the other as 6∗b , where a and b are integers. We also know that the product of the two numbers is 360 , so we can write

6∗a∗6∗b=360

or

36∗ab=360

which after dividing both sides by 36 gives us

which after dividing both sides by 36 gives usab=10

The only positive integer solutions for that are

The only positive integer solutions for that area=1,b=10

and

a=2,b=5

which means our possible pairs are 6,60 and 12,30

For both pairs, the LCM is easily seen to be 60.