Question

the LCM of Two number is 432 and their HCF is
36. If one of the numbers is 108, then find the
others
number​

Answer 1

Answer:

The second number is $144$.

Step-by-step explanation:

Let the numbers be $36$ and $x$.

It is given that the LCM and the HCF of the two numbers are $432$ and $108$ respectively.

LCM (Least common multiple):

LCM is an abbreviation for Least Common Multiple. A multiple is a number obtained by multiplying an integer by a whole number (greater than 0).

HCF (Highest common factor):

In mathematics, HCF stands for Highest Common Factor. HCF of two or more numbers is the biggest factor that divides the numbers.

We know that L.C.M × H.C.F $=$ Product of the two numbers

$432*36=108*x$

$x=\frac{432*36}{108}\\\\x=\frac{432}{3} \\\\x=144$

Therefore, the second number is $144$.

Answer 2

The other number = 144

Given :

• LCM of two number is 432 and their HCF is 36

• One of the numbers is 108

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 number is 432 and their HCF is 36

One of the numbers is 108

Step 2 of 2 :

Find the other number

We know that ,

HCF × LCM = Product of the numbers

Thus we get ,

$\displaystyle \sf{ 36 \times 432 = 108 \times Other \: number }$

$\displaystyle \sf{ \implies 108 \times Other \: number = 36 \times 432 }$

$\displaystyle \sf{ \implies Other \: number = \frac{36 \times 432}{108} }$

$\displaystyle \sf{ \implies Other \: number = \frac{432 }{3} }$

$\displaystyle \sf{ \implies Other \: number = 144}$

Hence the other number = 144

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