Question

the hcf of two numbers is 18 and their lcm is 8118. If one number is 198, find the other.​

Answer 1

Answer:

Let the other number be x

x×198=18×8118

x=18×8118/198

x=738

Answer 2

Answer :–

• The other number = 738.

Given :–

• Highest common factor (H.C.F.) = 18.
• Least common multiple (L.C.M.) = 8118.
• One number = 198.

To Find :–

• The other number.

Solution :–

Let,

The other number be x.

We know that,

⟶ L.C.M. × H.C.F. = One number × Other number (1)

Here given that,

• L.C.M. = 8118.
• H.C.F. = 18.
• One number = 198.

Now, substitute all the given values in equ. (1),

⟶ $8118 \times 18 = 198 \times x$

⟶ $146124 = 198x$

⟶ $\dfrac{ \cancel{146124}}{ \cancel{198}} = x$

Cut it by 2, we obtain

⟶ $\dfrac{ \cancel{73062}}{ \cancel{99}} = x$

Now, cut it by 3, we obtain

⟶ $\dfrac{\cancel{24354}}{ \cancel{33}} = x$

Again, cut it by 3, we obtain

⟶ $\dfrac{ \cancel{8118}}{ \cancel{11}} = x$

Now, cut it by 11, we obtain

⟶ $\dfrac{738}{1} = x$

⟶ $x = 738$

Hence,

The other number is 738.

Check :–

Put all the values in equation (1),

⟶ $8118 \times 18 = 198 \times 738$

⟶ $146124 = 146124$

Since, the L.H.S. and the R.H.S. are equal.

So, the value of other number is 738 is correct.

• L.H.S. = Left hand side.
• R.H.S. = Right hand side.