Question

The HCF and LCM of two numbers are 9 and 90 respectively. If one
number is 18, find the other.​

Answer 1

$\frak {Given} \begin{cases} \sf{H.C.F\:of\:two\:numbers = \bf{9}} \\ \sf{L.C.M\:of\:two\:numbers = \bf{90}} \\ \sf{One\:of\:the\;number\:is = \bf{18}} \end{cases}$

To find: Other number?⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

☯ Let's consider the other number be x.

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{L.C.M \times H.C.F = a \times b}}}}$

where, a and b are two numbers.⠀⠀

⠀⠀$\dag\;{\underline{\frak{Now,\: Substituting\:values\:in\:formula,}}}$

$:\implies\sf 90 \times 9 = 18 \times x \\\\\\:\implies\sf x = 9 \times \dfrac{\cancel{90}}{\cancel{18}} \\\\\\:\implies\sf x = 9 \times 5\\\\\\:\implies\boxed{\frak{\purple{x = 45}}}$

$\therefore\:{\underline{\sf{The\:other\:number\:is\: {\textsf{\textbf{45}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀

$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\: Additional \ Information \:\bigstar}}}}$

• HCF is the Highest common factor, the number which is present greatest number b/w two, three numbers.

• LCM is the Lowest common factor, the least divisible number.

Answer 2

Answer:

Given :-

• The HCF and LCM of two numbers are 9 and 90 respectively.
• One number is 18.

To Find :-

• What is the other number.

Solution :-

Let, the other number be x

Given :

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

We know that,

★ One number × Other number = HCF × LCM ★

According to the question by using the formula we get,

↦ 18 × x = 9 × 90

↦ 18x = 810

↦ x = $\sf{\cancel{\dfrac{810}{18}}}$

➠ x = 45

Hence, the other number is 45

$\therefore$ The other number is 45 .

Let's Verify :

⇒ 18 × x = 9 × 90

Put x = 45 we get,

⇒ 18 × 45 = 9 × 90

⇒ 810 = 810

➦ LHS= RHS

Hence, Verified ✔