Question

find the LCM and hcf of pairs of integers 336 and 54 , also find that LCM ×HCF => Product of the two numbers. ​

Answer 1

Step-by-step explanation:

LCM ( 336, 54 ) = 2⁴ × 3 × 7 = 3024. HCF ( 336, 54 ) = 2 × 3 = 6. Now, LCM × HCF = Product of two numbers

Answer 2

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

$\red{ \bf \: Prime \: Factorization \: of \: 336}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:336\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:168\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:84\:}}\\\underline{\sf{2}}&\underline{\sf{\:\:42\:}}\\\underline{\sf{3}}&\underline{\sf{\:\:21\:}}\\\underline{\sf{7}}&\underline{\sf{\:\:7\:}}\\\underline{\sf{}}&{\sf{\:\:1\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\bf\implies \:336 = {2}^{4} \times 3 \times 7$

$\red{ \bf \: Prime \: Factorization \: of \: 54}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:54\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:27\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:9\:}}\\\underline{\sf{3}}&\underline{\sf{\:\:3\:}}\\\underline{\sf{}}&{\sf{\:\:1\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\bf\implies \:54 = {3}^{3} \times 2$

So, we have prime factorization of 336 and 54 as

$\bf\longmapsto\:336 = {2}^{4} \times 3 \times 7$

$\bf\longmapsto\:54 = {3}^{3} \times 2$

Thus,

$\bf\implies \:HCF(336, 54) = 2 \times 3 = 6$

$\bf\implies \:LCM(336, 54) = {2}^{4} \times {3}^{3} \times 7 = 3024$

Now,

$\bf :\longmapsto\:LCM \times HCF = 3024 \times 6 = 18144$

Let

• a = 336

• b = 54

So,

$\bf :\longmapsto\:a \times b = 336 \times 54 = 18144$

$\bf :\implies\:LCM \times HCF = a \times b$