Question

If the bigger number is 90 in the numbers having LCM 5670 and HCF 9 find the smaller number ​

Answer 1

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Let "a" be the required number

Given

• One of the two numbers is 90

• HCF(90,a) = 9

• LCM (90,a) = 5670

Relationship between the numbers and their HCF and LCM is given as:

$\huge{\sf{lcm \: \times \: hcf \: = \: x.y}}$

Putting the values,we get:

$\sf{5670 \times 9 = 90a} \\ \\ \implies \: \sf{10a = 5670} \\ \\ \implies \: \sf{ \cancel{10}a = \cancel{5670}} \\ \\ \implies \: \huge{ \sf{a = 567}}$

Thus,the required number is 567

Answer 2

Given:

LCM of two numbers =5670

HCF of two numbers =9

one of the numbers=90

To find:

The other number

Explanation:

Let the other number be x

we know that

$\boxed{\underline{\bf LCM×HCF=product \: of \: numbers }}$

substituting

$= > 5670 \times 9 = 90 \times x \\ \\ = > x = \dfrac{5670 \times 9}{90} \\ \\ = > \boxed{ \sf \: x = 567 }$

Therefore the other number is 567