Question

If lcm and hcf of two numbers are equal and product of two numbers is 2916, find their lcm

Answer 1

LCM × HCF = Product of two numbers
Acording to the given condition LCM = HCF
Let LCM = HCF = X
Hence by formula
X × X = 2916
X^2 = 2916 = (54)^2
Hence X = 54
i.e. LCM = HCF = 54

Answer 2

Answer:

LCM of two numbers x and y is the Least Common Multiple

and the  HCF of two numbers is the Highest Common Factor.

The product of the LCM and HCF of two numbers is the same as the product of the numbers themselves i.e

$LCM \times HCF = x \times y$         ......[1]

Given: LCM =HCF  also the product of two numbers is 2916. i.e, $x \times y$ = 2916.

Substitute these in equation[1]

⇒ $LCM \times LCM = 2916$

$LCM^2 =2916$ or

$LCM=\sqrt{2916}=54$

Therefore, the LCM of two numbers is, 54