Question

1. The LCM and HCF of two numbers are 120 and 6 respectively. If one of the number is 30 then
Find the other number​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :

• We have been given two numbers whose LCM and HCF are 120 and 6 respectively
• One of the Number is 30

To Find :

• We have to find the second number

Concept Used :

The Product of HCF and LCM of any two numbers is always equal to the Product of that numbers itself

$\boxed{\sf{Product \: of \: Numbers = LCM \times HCF}}$

Solution :

Let the second number be = x

Since we have been given that

• HCF = 6
• LCM = 120
• One number = 30

Using the above mentioned concept in the given Question

$\longrightarrow \sf{( x ) \times 30 = LCM \times HCF}$

$\longrightarrow \sf{( x ) \times 30 = 120 \times 6}$

$\longrightarrow \sf{30x = 720}$

$\longrightarrow \sf{x = \dfrac{720}{30}}$

$\longrightarrow \underline{\boxed{\sf{x = 24}}}$

Hence , the second number is 24

$\large{\underline{\boxed{\sf{\blue{Second \: Number = 24}}} }}$

$\large{\gray{\underline{\underline{\sf{Extra \: Information:}}}}}$

• LCM is known as Least common multiple , can be defined as the smallest positive number that is easily divisible by both the given numbers
• HCF is known as Highest common Factor , can be defined as the greatest number which can divide both the given number easily
• Example : 2 and 4 , where LCM is 4 and HCF of given number is 2