Question

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the integers:
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
(iv) 404 and 96

Answer 1

TO FIND: LCM and HCF of following pairs of integers

TO VERIFY:

(i) 26 and 91

Let us first find the factors of 26 and 91

We know that,

$$\begin{gathered} \mathrm{L}.\mathrm{C}.\mathrm{M}\times \mathrm{H}.\mathrm{C}.\mathrm{F}=\mathrm{First}\mathrm{number}\times \mathrm{Second}\mathrm{number} \\ \Rightarrow 182\times 13=26\times 91 \\ \Rightarrow 2366=2366 \end{gathered}$$

Hence verified

(ii) 510 and 92

Let us first find the factors of 510 and 92

We know that,

Hence verified

(iii) 336 and 54

Let us first find the factors of 336 and 54

We know that,

Hence verified

(iv)
$$\begin{gathered} 404=2\times 2\times 101 \\ 96=2\times 2\times 2\times 2\times 2\times 3 \\ \mathrm{LCM}=2\times 2\times 2\times 2\times 2\times 3\times 101=9696 \\ \mathrm{LCM}=9696 \\ \mathrm{HCF}=2\times 2=4 \\ \mathrm{Product}\mathrm{of}\mathrm{numbers}=96\times 404=38784 \\ \mathrm{LCM}\times \mathrm{HCF}=4\times 9696=38784 \\ \mathrm{Hence},\mathrm{LCM}\times \mathrm{HCF}=\mathrm{Product}\mathrm{of}\mathrm{numbers} \end{gathered}$$