Question

The HCF and LCM of two number are 4 and 60. If one number is the multiple of other number find the numbers.

Answer 1

Answer:

If x and y are two numbers then,

Rule : HCF * LCM = x * y

So, by above logic,

HCF * 60 = 12 * y

But,

HCF <= 12 (if 12 is the smaller number)  

or

HCF <= y (if y is the smaller number)

and

LCM >= 12 (if 12 is the bigger number)

LCM >= y (if y is the bigger number)

i.e.

60 >= 12 (true)

or

LCM >= y (if y is the bigger number)

So,

HCF <= 12 <= LCM(i.e. 60) - (1)

HCF <= y <= 60 - (2)

By taking all considerations above,

If y < 12

Then

y = 5 or 10 (found by factors of 60 which produce 60 as LCM with 12).

Else if Y > 12

Then

y = 15 or 20 or 30 or 60 (found by factors of 60 which produce 60 as LCM with 12).

Therefore ,

For,

For y = 5

HCF = 1

For y =10

HCF = 2

For y = 15

HCF = 3

For y = 20

HCF = 4

For y = 30

HCF = 6

For y = 60

HCF = 12

This was my observation

Thank You.

I had to do a lot of hard work

Please mark this answer as BRAINLIEST