Question

Sum of two numbers is 31 and its product is 238 then whalt will be lcm

Answer 1

Answer:

238

Step-by-step explanation:

Let us factorize 238.

238= 2x7x17

By trial and error, we get 14 and 17, which fits the criteria.

Since 17 is prime, the HCF is 1.

Thus, LCM= Product ÷ HCF= 238÷1= 238

Answer 2

Answer:

the required numbers be x and y.

Hence, according to the given information:

x + y = 31. ...... (1)

xy = 238 .........(2)

Since

\begin{lgathered}( {x - y})^{2} = ( {x + y})^{2} - 4xy \: ....(3) \\ from \: equations \: (1) \: (2) \: and \: (3) \\ ( {x - y})^{2} = ({31})^{2} - 4 \times 238 \\ ( {x - y})^{2} = 961 - 952 \\ ( {x - y})^{2} = 9 \\ {x - y} = 3 \: \: .....(4) \\ adding \: (1) \: and \: (4) \: we \: find \\ 2x = 34 \\ x = 17 \\ y = 14 \\ lcm \: of \: 17 \: and \: 14 \: = 17 \times 14 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 238\end{lgathered}

(x−y)

2

=(x+y)

2

−4xy....(3)

fromequations(1)(2)and(3)

(x−y)

2

=(31)

2

−4×238

(x−y)

2

=961−952

(x−y)

2

=9

x−y=3.....(4)

adding(1)and(4)wefind

2x=34

x=17

y=14

lcmof17and14=17×14

=238