Question

Mohit is thinking of two numbers. Their greatest common factor is 6. Their least common multiple is 36. One of the numbers is 12. What is the other number

Answer 1

Let the unknown no. be x

Given that the other no. is 12

Given

HCF = 6

LCM = 36

We know that 

Product of numbers =  HCF × LCM

⇒ 12 × x = 6× 36

⇒ 12x = 216

⇒ x = 216/12

⇒ x = 18

∴ The other number is 18

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Answer 2

Given,

Mohit is thinking of two numbers.

One of the numbers is 12.

Their greatest common factor is 6.

Their least common multiple is 36.

To find,

The other number.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the other number is n.

Mathematically,

If x and y are two numbers, then,

x × y = (H.C.F. of x and y)×(L.C.M. of x and y)

{Statement-1}

According to the question;

The H.C.F. of both the numbers that Mohit is thinking of = Greatest common factor of both numbers = 6

The L.C.M. of both the numbers = least common multiple = 36

Now, according to the question;

The product of the two numbers that Mohit is thinking of = (H.C.F. of both numbers)×(L.C.M. of both numbers)

=> 12 × n = 6 × 36

=> n = (6×36)/12 = 18

=> n = 18

=> the other number = 18

Hence, the other number is 18.