Question

(a) The LCM and HCF of two numbers are 252 and 6 respectively. if one of the number is 42 find the other number.

Answer in detail​

Answer 1

there is a property which states:-

LCM × HCF = first number × second number

let the other number be = x

So,    252 × 6 = 42 × x

⇒ 1512 = 42x

⇒1512/42 = 42x/42               ( dividing both the sides by 42)

⇒ 36 = x

Hence, other number is 36

Hope you find it helful  :)

Answer 2

The other number = 36

Given :

• The LCM and HCF of two numbers are 252 and 6 respectively

• One of the numbers is 42

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 and HCF of two numbers are 252 and 6 respectively

One of the numbers is 42

Step 2 of 2 :

Find the other number

We know that ,

HCF × LCM = Product of the numbers

Thus we get ,

$\displaystyle \sf{ 6 \times 252 = 42 \times Other \: number }$

$\displaystyle \sf{ \implies 42 \times Other \: number =6 \times 252 }$

$\displaystyle \sf{ \implies Other \: number = \frac{6 \times 252}{42} }$

$\displaystyle \sf{ \implies Other \: number = \frac{252 }{7 } }$

$\displaystyle \sf{ \implies Other \: number =36 }$

Hence the other number = 36

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