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# Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF $=$ Product of the integers:

(i) 26 and 91

**Given:**

Given pair of integers is 26 and 91.

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**To do:**

Here we have to find the LCM and HCF of the given pair of integers and then verify that LCM $\times$ HCF $=$ Product of the integers.

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**Solution:**

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__Calculating LCM and HCF using prime factorization method__:

Writing the numbers as a product of their prime factors:

Prime factorisation of 26:

- $2\ \times\ 13\ =\ 2^1\ \times\ 13^1$

Prime factorisation of 91:

- $7\ \times\ 13\ =\ 7^1\ \times\ 13^1$

Multiplying the highest power of each prime number these values together:

$2^1\ \times\ 13^1\ \times\ 7^1\ =\ 182$

LCM(26, 91) $=$ **182**

Multiplying all common prime factors:

$13^1\ =\ 13$

HCF(26, 91) $=$ **13**

Now, verifying that LCM $\times$ HCF $=$ Product of the integers:

LCM $\times$ HCF $=$ Product of the integers

182 $\times$ 13 $=$ 26 $\times$ 91

2366 $=$ 2366.