Question

1. For each of the following pairs of numbers verify that product of numbers is equal to the product of their HCF and LCM.
(a) 10,15​

Answer 1

Gɪᴠᴇɴ

Two numbers are, 10 & 15

Tᴏ ꜰɪɴᴅ

We have to verify that product of numbers is equal to product of LCM & HCF

Sᴏʟᴜᴛɪᴏɴ

First we will find LCM of 10,15 by prime factorization :

5|10,15

|2,3

So, LCM = 5 × 2 × 3

LCM = 30

Now finding HCF of 10 & 15 :

➝ 10 = 2 × 5

➝ 15 = 3 × 5

So, HCF = 5

Tʜᴇʀᴇꜰᴏʀᴇ, LCM & HCF are 30 & 5 respectively.

Now verification :

⟼ LCM × HCF = Product of 2 numbers

⟼ 30 × 5 = 10 × 15

⟼ 150 = 150

Hence, LHS = RHS [Hence Verified! ]

Answer 2

Answer:

$\bigstar\:\underline{\sf LCM}\qquad\qquad\qquad\quad\bigstar\:\underline{\sf HCF}\\\\\begin{tabular}{l|c}\sf5&\textsf{10, 15}\\\cline{1-2}&\textsf{2, 3}\end{tabular}\qquad\qquad\quad\begin{tabular}{|c|}\cline{1-2}\sf 10 = 1\times\sf2\times5\\\sf15 = 1\times\sf3\times5\\\cline{1-2}\end{tabular}\\\\\sf LCM =5\times2\times3\qquad\quad\sf HCF = 1\times5\\\textsf{LCM (10, 15) = 30}\qquad\:\textsf{HCF (10, 15) = 5}$

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf LCM \times HCF = Product\:of\: Number\\\\\\:\implies\sf 30 \times 5=10 \times 15\\\\\\:\implies\underline{\boxed{\sf 150=150}}$