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If LCM of two numbers is 156 and HCF of the same numbers is 26. If the sum of the numbers is 130, the value of larger number is _______
- A78
- B62
- C42
- D88
Answer not set
Discussion 1
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CCommunity
By the data given in the question,
LCM (a, b) = 156
HCF (a, b) = 26
a + b = 130
⇒ b = 130 - a ----(I)
By using the equation,
LCM (a, b) × HCF (a ,b) = a × b
⇒ 156 × 26 = a × (130 - a) [substitute the value of Eq(I)]
⇒ 4056 = 130a - a2
⇒ a2 - 130a + 4056 = 0
⇒ a2 - 52a - 78a + 4056 = 0
⇒ (a - 52)(a - 78) = 0
Take, a = 78
⇒ b = 130 - 78 = 52
∴ value of larger number = 78
LCM (a, b) = 156
HCF (a, b) = 26
a + b = 130
⇒ b = 130 - a ----(I)
By using the equation,
LCM (a, b) × HCF (a ,b) = a × b
⇒ 156 × 26 = a × (130 - a) [substitute the value of Eq(I)]
⇒ 4056 = 130a - a2
⇒ a2 - 130a + 4056 = 0
⇒ a2 - 52a - 78a + 4056 = 0
⇒ (a - 52)(a - 78) = 0
Take, a = 78
⇒ b = 130 - 78 = 52
∴ value of larger number = 78