Question

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

Answer 1

Product of two numbers = xy = 180

HCF of x and y = 3

we have to find out LCM of x and y.

We know that :-

$\boxed{ \boxed{ \tt \large\: L.C.M \: of \: two \: given \: \: numbers\times H.C.F\: of \: two \: given \: numbers = product \: of \: numbers}}$

Let LCM be L.

According to the question :-

$\tt \longrightarrow L \times 3 = 180 \\ \\ \tt \longrightarrow L = \frac{180}{3} \\ \\ \tt \longrightarrow L = \frac{60}{1} \\ \\ \tt \longrightarrow L = 60$

Therefore , LCM of x and y = 60

Answer : 60

$\red {\tt \large Verification\: Of \: Answer :}$

To verify our answer , we will find product of HCF and LCM. If we get product as 180 then our answer is correct.

HCF = 3

LCM = 60

$\tt \rightarrow 3\times60$

$\tt \rightarrow 180$

Hence verified

Therefore, our answer is correct.