Question

please help me. The GCF and LCM of two numbers are 9and90 respectively if one of the numbers is 18 find the other number.​

Answer 1

Answer:

Given :-

• The GCF and LCM of two numbers are 9 and 90 respectively.
• One of the numbers is 18.

To Find :-

• What is the other number.

Solution :-

Let, the other number be x

Given :

• GCF = 9
• LCM = 90
• One number = 18

As we know that :

➲ One number × Other number = GCF × LCM

According to the question by using the formula we get,

↦ 18 × x = 9 × 90

↦ 18x = 810

↦ x = 810/18

➠ x = 45

∴ The other number is 45 .

_______________________

VERIFICATION :

↦ One number × Other number = GCF × LCM

↦ 18 × x = 9 × 90

↦ 18x = 810

By putting x = 45 we get,

↦ 18(45) = 810

↦ 18 × 45 = 810

➦ 810 = 810

Hence, Verified .

Answer 2

$\clubs \: \: \: { \large{ \color{navy}{ \underline{ \sf{Question}}}}}$

• The GCF and LCM of two numbers are 9and90 respectively if one of the numbers is 18 find the other number.

$\clubs \: \: \: { \large{ \color{navy}{ \underline{ \sf{Solution}}}}}$

$\blacktriangleright \: \: \sf{ \large{ \underline{ \underline{ \color{red}{Given : }}}}}$

• GCF and LCM of two numbers 9 and 90 respectively.
• and one number is 18.

$\blacktriangleright \: \: \sf{ \large{ \underline{ \underline{ \color{red}{ To Find: }}}}}$

• The Other Number .

$\longmapsto{ \underline { \boxed{ \color{green}{ \sf{Let \: the \: other \: Number \: be \: x}}}}}$

• Here we use the formula :

$\sf{ \underbrace{ \color{purple}{one \: number \times other \: number \: = GCF \times LCM}}}$

Here :-

• GCF → 9
• LCM → 90
• one number → 18

By Substituting the values in the above formula.

We get,

$\longmapsto \sf{ \color{red}{18 \times x = 9 \times 90}}$

$\longmapsto \sf{ \color{red}{18 \: x = 810}}$

$\longmapsto \sf{ \color{red}{x \: = \: \frac{180}{18} }}$

$\longmapsto \sf{ \color{red}{x \: = \: \cancel \frac{180}{18} \: = 45 }}$

$\longmapsto { \underline{ \boxed{\sf{ \color{darkblue}{x = 45}}}}}$

$\qquad \therefore \: \sf{ \underline{ \underline {The \: other \: number \: is \: 45}}}$

$\blacktriangleright \: \: \sf{ \large{ \underline{ \underline{ \color{red}{Verification : }}}}}$

• By putting the values in the above Equation

$\sf{ \underbrace{ \color{purple}{one \: number \times other \: number \: = GCF \times LCM}}}$

$\longmapsto \sf{18 \times x = 9 \times 90}$

$\longmapsto \sf{18 \: x = 810}$

• Now the Other Number $\sf{ \underline{x = 45}}$So we get ,

$\longmapsto \sf{18 \: (45)= 810}$

$\longmapsto \sf{810= 810}$

• Hence LHS = RHS

$\qquad \spades \: \: \sf{hence \: verified}$