Question

two number ratio is 5:7 and their H.c.f.is13 find the two numbers​

Answer 1

Answer:

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Step-by-step explanation:

Let the numbers be A and B.

So A:B= 5:7

Since hcf, the greatest common divisor is 13, the two numbers will be the multiples of 5 and 7 respectively.

Other than hcf , no other number will be common to both numbers.

So A= 13 x 5= 65 and

B= 13 x 7= 91

So the numbers are 65 and 91

Answer 2

Given

• two number ratio is 5:7
• their H.c.f. is 13

To Find

• two numbers

Concept used

• Product of two numbers=HCF×LCM

Solution

We have the two numbers ratio

but for this we need two numbers

so

we let two numbers be 5x and 7x respectively

First HCF is the highest common factors of the numbers

So here hcf is x

And we know that

Product of numbers=HCF × LCM

Here

• Number 1=5x=5×13=65
• Number 2=7x=7×13=91
• HCF=x=13
• LCM=?

Putting values

$\rm \: 65 \times 91 = 13 \times y \\ \\ \rm \: \frac{65 \times 91}{13} = y \\ \\ \implies \rm \boxed{ \bf \: y = 455}$

So LCM=455

Numbers are 65,91 because we multiply HCF in both the numbers

Verification

Product of Numbers=Product of HCF AND LCM

LHS

$\rm \: 65 \times 91 \\ \\ \underline{ \boxed{\bf \:LHS = 5915 }}$

RHS

$\rm \: 455 \times 13 \\ \\ \rm \boxed{ \bf \: RHS = 5915}$

LHS=RHS

HENCE PROVED