Question

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find the HCF and LCM of 16 and 20 and verfiy the hcf×lcm= 1 number × 2 number



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Answer 1

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Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

LCM is 80 and HCF is 4

$\textbf{\underline{\underline{Explanation :-}}}$

$\text{\underline{Given :}}$

The numbers = 16 and 20

$\text{\underline{To find :}}$

The LCM and HCF of given Numbers and Verification of the Relation between HCF and LCM.

$\text{\underline{Solution :}}$

LCM of 16 and 20 :

$\begin{array}{r|l} 2 & 16, 20 \\\cline{1-2} 2 & 8,10 \\\cline{1-2} 2 & 4,5 \\ \cline{1-2} 2 & 2,5 \\\cline{1-2} 5 &1,5 \\\cline{1-2} & 1,1 \end{array}$

LCM = 2 × 2 × 2 × 2 × 5

→ 80

$\boxed{\sf{\red{LCM = 80}}}$

HCF of 16 and 20 :

Prime Factorization of 16

$\begin{array}{r|l}2 & 16 \\\cline{1-2} 2 & 8 \\\cline{1-2} 2 & 4\\ \cline{1-2} 2 & 2 \\\cline{1-2} & 1 \end{array}$

Prime Factorization of 20

$\begin{array}{r|l}2 & 20 \\\cline{1-2} 2 & 10 \\\cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

16 = 2 × 2 × 2 × 2

20 = 2 × 2 × 5

HCF = 2 × 2 = 4

$\boxed{\sf{\red{HCF = 4}}}$

Verification of the Relation between HCF and LCM :

$\boxed{\tt{HCF \times LCM = Product\:of\:2\:numbers}}$

HCF = 4

LCM = 80

One number = 16

Second Number = 20

$\tt{\implies}4 \times 80 = 16 \times 20$

$\tt{\implies}320 = 320$

Both sides are equal.

Hence,

Verified.