Question

If xy=180 and HCF(x,y)=3, then find the LCM(x,y).​

Answer 1

Given

• Two variables x and y
• Product of these variables is 180
• HCF of these variables is 3

To Find

• LCM of these variables

Solution

With the theorem we know that product of HCF and LCM is equal to product of the number

• So first we write the equation properly

• Then we equate it or simplify it then we find LCM of these variables

$\rm \: product \: of \: two \: numbers = x \times y \\ \\ \boxed{ \bf \: xy = 180}$

$\rm product \: of \: HCF \: and \:LCM = 3 \times LCM$

Since product of HCF AND LCM=Product of two numbers

Therefore

$\rm \: 3 \times LCM = xy \\ \\ \rm \implies 3 \times LCM = 180 \: \: \: \: \: \: \\ \\ \implies \rm \: LCM = \frac{180}{3} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \boxed{ \huge{ \bf\: LCM = 60}}$

LCM of the variables x and y is 60 is the answer of this above question

Answer 2

Product of two numbers = LCM × HCF

x × y = 3 × LCM

180 = 3 × LCM

LCM= 180÷3

= 60