the HCF and LCM of two number is 12and72 find the numbers .
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Answer:
x=24 or x=36. If x=24, then y=36 and if x=36, then y=24.
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Given:
HCF = 12
LCM = 72
Sum of number = 60
Concept used:
Product of number = HCF × LCM
Calculation:
Let the 1st number be x & 2nd number will be (60 - x)
Product of number = HCF × LCM
⇒ x × (60 - x) = 12 × 72
⇒ 60x - x2 = 864
⇒ x2 - 60x + 864 = 0
⇒ x2 - 24x - 36x + 864 = 0
⇒ x(x - 24) - 36(x - 24) = 0
⇒ (x - 24)(x - 36) = 0
⇒ (x - 24) = 0 or (x - 36) = 0
⇒ x = 24 or x = 36
∴ The one of the number is 24.
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