Question

find the LCM and HCF of the following pairs of integers and verify that LCM into HCF is equal to product of the two that is 26 and 91l​

Answer 1

Answer:

Step-by-step explanation:

Correct Question :-

Find the LCM and HCF of the following pairs of integers and verify that LCM into HCF is equal to product of the two that is 26 and 91.

Given Numbers :-

First Number = 26

Second Number = 91

Solution :-

The prime factor of 26 and 91 :-

⇒ 26 = 2 × 13

⇒ 91= 7 × 13

LCM of 26 and 91 = 2 × 7 × 13 = 182

HCF of 26 and 91 = 13

Verification :-

⇒ LCM × HCF = 26 × 91 = 2366

⇒ Product of integers = 182 × 13 = 2366

⇒ LCM × HCF = product of the integers.

⇒ 2366 = 2366

Hence, verified

Important Information :-

LCM of two or more numbers = product of the greatest power of each prime numbers.

Answer 2

Answer:

Given:-

• Numbers = 26 & 91

To find LCM:-

$\begin{array}{r | l } 2 & 26,91 \\ \cline{2 - 2} 7 & 13,91 \\\cline{2 - 2} 13 & 13,13 \\\cline{2 - 2} & 1,1 \end{array}$

$\therefore\sf LCM = 2 * 7 * 13 \\\\\therefore\sf LCM = {\boxed{\sf\green{182}}}$

$\rule{200}{1}$

$\sf Now, 26 = 1 * 26 \\\\\sf \: \: \: \: \: \: \: \:\: \: \: \: \: \:\: \: = 2 * 13$

$\sf Again,91 = 1 * 91 \\\\\sf \: \: \: \: \: \: \: \:\: \: \: \: \:\:\: \: \: = 7 * 13$

$\therefore\sf HCF = 1 * 13 \\\\\therefore\sf HCF ={\boxed{\sf\green{13}}}$

$\therefore\sf LCM \: \& \: HCF = \large{\boxed{\sf\pink{182 \: \& \: 13 }}}$

$\rule{100}{1}$

To verify:-

$\sf LCM * HCF = Product \: of \: 26 \: \& \: 91$

$\large\bold{Verification:-}$

$\sf LCM \times HCF = 26 \times 91 \\\\\Rightarrow\sf 182 \times 13 = 2366 \\\\\Rightarrow\sf\blue{2366 = 2366 \: \: \: [Verified!]}$

$\therefore\sf\pink{LCM \times HCF = Product \: of \: numbers \: \: [Hence \: verified!] }$