Question

if least common multiple of two numbers is 225 and the highest common factor is 5 then find the numbers when one of the numbers is 25​

Answer 1

• The other number = 45

• The two numbers are 25 & 45

Given :

• The least common multiple of two numbers is 225 and the highest common factor is 5

• One of the numbers is 25

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 the least common multiple of two numbers is 225 and the highest common factor is 5

HCF = 5 & LCM = 225

One of the numbers is 25

Step 2 of 2 :

Find the other number

We know that ,

HCF × LCM = Product of the numbers

Thus we get ,

$\displaystyle \sf{ 5 \times 225 = 25 \times Other \: number }$

$\displaystyle \sf{ \implies 25 \times Other \: number =5 \times 225 }$

$\displaystyle \sf{ \implies Other \: number = \frac{5 \times 225}{25} }$

$\displaystyle \sf{ \implies Other \: number = \frac{225 }{5} }$

$\displaystyle \sf{ \implies Other \: number =45 }$

Hence the other number = 45

Also two numbers are 25 and 45

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