Question

LCM of two prime numbers is 221. If one number is 13, what is the other number?

Answer 1

Answer:

LCM=221

HCF=1 (two numbers are co prime numbers)

lcm × hcf = first number × second number

221 × 1 = 13 × second number

second number = 221 / 13= 17

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Answer 2

The other number = 17

Given :

• LCM of two prime numbers is 221.

• One number is 13

To find :

The other number

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that LCM of two prime numbers is 221.

One number is 13

Since two numbers are prime

So HCF of two numbers = 1

Step 2 of 2 :

Find the other number

We know that ,

HCF × LCM = Product of the numbers

Thus we get ,

$\displaystyle \sf{ 1 \times 221 = 13 \times Other \: number }$

$\displaystyle \sf{ \implies 13 \times Other \: number =1 \times 221 }$

$\displaystyle \sf{ \implies Other \: number = \frac{1 \times 221}{13} }$

$\displaystyle \sf{ \implies Other \: number = \frac{221 }{13} }$

$\displaystyle \sf{ \implies Other \: number =18 }$

Hence the other number = 17

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