Question

Find the LCM and HCF of the following pair of integers and verify that LCM$\times$HCF$=$ the product of the two numbers.

$26$and $91$

Answer 1

Step 1: Find the L.C.M. and H.C.F of given two numbers.

The given integers are$26$and $91$

Firstly, let us find out the prime factors of $26$ and $91$

The prime factors of $26=2\times 13$

The prime factors of $91=7\times 13$

$\Rightarrow$. $L.C.M.(26,91)=2\times 7\times 13=182$

$\Rightarrow$ $H.C.F.(26,91)=13$

Step 2: Compare it with the product of H.C.F and L.C.M.

$$\begin{gathered} L.C.M\times H.C.F=182x13 \\ L.C.M\times H.C.F=2366...\left(1\right) \end{gathered}$$

And, Product of the two integers $=26x91=2366...\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$

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

Hence verified.

The LCM $(26,91)=182$ and the H.C.F.$(26,91)=13$

Hence LCM$\times$HCF $=$ Product of the integers$=2366$