Question

the product of two number is 1260 and their HCF is 12 find the LCM​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The LCM is 105

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Product of the numbers = 1260

HCF = 12

To Find :

The LCM

Solution :

★ $\boxed{\sf{HCF \times LCM = Product\:of\:2\:numbers}}$

Consider the LCM as x

$\sf{\implies} \: 12 \times x = 1260$

$\sf{\implies} \: 12x = 1260$

$\sf{\implies} \: x = \dfrac{1260}{12}$

$\sf{\implies} \: x = 105$

$\therefore$ The LCM is 105

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\sf{\implies} \: 12 \times 105 = 1260$

$\sf{\implies} \: 1260 = 1260$

$\therefore$ The LCM is 105

Answer 2

SOLUTION ;

Given :-

The product of two numbers is 1260

The HCF of the numbers is 12

To be found :

The LCM of the numbers

As we know,

HCF × LCM = product of two numbers

So,

⇒ 12 × LCM = 1260

[∵ HCF = 12, product of two numbers = 1260]

⇒ LCM = 1260 ÷ 12

[ transporting 12 to RHS ]

⇒ LCM = 105

Hence,

The LCM of two numbers is 105

 

 

Verification :

LHS = HCF × LCM

       = 12 × 105

       = 1260 = RHS (product of two numbers)

∴verified