Question

the H.C.F and L.C.M of two numbers is 24 and 240 respectively . if one of the numbers is 120,find the other number with method

Answer 1

Answer:

Given :-

• The H.C.F and L.C.M of two numbers is 24 and 240 respectively.
• One of the numbers is 120.

To Find :-

• What is the other number.

Solution :-

Let,

$\mapsto \bf Other\: Number =\: x$

Given :

• H.C.F = 24
• L.C.M = 240
• One of the number = 120

As we know that :

$\footnotesize \bigstar\: \: \sf\boxed{\bold{\pink{Product\: of\: two\: Number =\: H.CF \times L.CM}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf 120(x) =\: 24 \times 240$

$\implies \sf 120x =\: 5760$

$\implies \sf x =\: \dfrac{\cancel{5760}}{\cancel{120}}$

$\implies \sf x =\: \dfrac{48}{1}$

$\implies \sf\bold{\red{x =\: 48}}$

$\therefore$ The other number is 48 .

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VERIFICATION :-

$\leadsto \sf 120x =\: 24 \times 240$

By putting x = 48 we get,

$\leadsto \sf 120(48) =\: 5760$

$\leadsto \sf\bold{\purple{5760 =\: 5760}}$

$\leadsto \sf\bold{\green{L.H.S =\: R.H.S}}$

HENCE VERIFIED !!

Answer 2

• As per the data given in the question, we have to determine the required number.

       Given data:- HCF=$24$ and LCM =$240.$    

        To find:- the other number=?

        Solution:-

        Let the required number be $x.$

       As, we know that,

       The Product of two numbers is HCF×LCM.

          $\begin{array}{l}\Rightarrow 120\times x=24\times240 \\\Rightarrow x=\frac{24\times240}{120} \\\Rightarrow x=48.\end{array}$

        Hence, the other number is $48.$