Question

दो संखायों का महत्तम समवर्तक और लघुत्तम समवर्तक 12तथा 72है यदि इन संख्या का योग 60है तो छोटी संख्या क्या होगी
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Answer 1

Answer:

✡24 ☑

Step-by-step explanation:

Given⤵

• HCF and LCM of two number is 12 and 72.
• Sum of numbers is 60.

To find ⤵

• Smaller number.

Solution ⤵

⚫We know that

LCM×HCF= Products of number

➡Products of number= 12×72

➡Products of number= 864.

➡Sum of number=60.

⚫Let the numbers are x and y.

➡x×y= 864 ...(i) or

➡x=864/y

➡x+y=60 ...(ii)

⚫Putting the value of x in equation (ii), we get

$➡ \frac{864}{y} + y = 60\\ ➡ \frac{864 + {y}^{2} }{y} = 60 \\ ➡864 + {y}^{2} = 60y \\➡ {y}^{2} - 60y + 864 = 0 \\ ➡ {y}^{2} - 36y - 24y + 864 = 0 \\ ➡y(y - 36) - 24(y - 36) = 0 \\ ➡(y - 36)(y - 24) = 0 \\ ➡y = 36 \: or \: y = 24$

✅Hence, the number are 24 and 36 . Smaller number is 24.

Hope this is helpful to you!