Question

find the LCM and HCF of 332 and 24 and verify that product of number is equal to the product LCM and hcf​

Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Solution-}}$

$\red{\bf :\longmapsto\:Prime \: factorization \: of \: 332}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:332\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:166 \:\:}} \\ {\underline{\sf{83}}}& \underline{\sf{\:\:83 \:\:}} \\ {\sf{}}&\underline{\sf{\:\:1\:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

$\red{\bf :\longmapsto\:Prime \: factorization \: of \: 332 = {2}^{2} \times 83 }$

$\blue{\bf :\longmapsto\:Prime \: factorization \: of \: 24}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:24\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:12 \:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:6 \:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:3 \:\:}} \\{\sf{}}&\underline{\sf{\:\:1\:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

$\blue{\bf :\longmapsto\:Prime \: factorization \: of \: 24 = {2}^{3} \times 3}$

So,

$\green{\bf :\longmapsto\:HCF(332, 24) = {2}^{2} = 4}$

and

$\green{\bf :\longmapsto\:LCM(332, 24) = {2}^{3} \times 3 \times 83= 1992}$

Verification

Consider,

$\green{\sf :\longmapsto\:LCM(332, 24) \times HCF(332, 24)= 1992 \times 4 = 7968}$

Also,

$\rm :\longmapsto\:Let \: a = 332 \: and \: b = 24$

So,

$\red{\bf :\longmapsto\:a \times b}$

$\red{\rm :\longmapsto\:\bf \: 332 \times 24 = 7968}$

Hence,

$\: \: \: \underbrace{\boxed{ \rm \: HCF(332, 24) \times LCM(332, 24) = 332 \times 24}}$

Additional Information :-

Let us assume two natural numbers a and b then

• 1. HCF(a, b) < = (a, b)

• 2. LCM (a, b) > = (a, b)

• 3. HCF always divides LCM.