The LCM of two numbers is 6 times their HCF. If one of them is 45 and

1.	The LCM of two numbers is 6 times their HCF. If one of them is 45 and the sum of HCF and LCM is 315, find the other number.A. 190B. 360C. 270D. 3001. B2. A3. C4. D
Answer» Correct Answer - Option 3 : C Given: The LCM of two numbers is 6 times their HCF. One of them is 45 and the sum of HCF and LCM is 315. Formula used: LCM × HCF = N₁ × N₂ LCM = least common factor, HCF = Heighest common factor N₁ = first number, N₂ = second number Calculation: According to the question, N₁ = 45 LCM = 6 HCF LCM + HCF = 315 ⇒ 6 × HCF + HCF = 315 ⇒ 7 HCF = 315 ⇒ HCF = 315/7 ⇒ HCF = 45 ⇒ LCM = 6 × HCF ⇒ LCM = 6 × 45 = 270 Then, LCM × HCF = N₁ × N₂ ⇒ 270 × 45 = 45 × N₂ ⇒ N₂ = 270 ∴ The other number is 270.

The LCM of two numbers is 6 times their HCF. If one of them is 45 and the sum of HCF and LCM is 315, find the other number.A. 190B. 360C. 270D. 3001. B2. A3. C4. D

Answer» Correct Answer - Option 3 : C

Given:

The LCM of two numbers is 6 times their HCF.

One of them is 45 and the sum of HCF and LCM is 315.

Formula used:

LCM × HCF = N₁ × N₂

LCM = least common factor, HCF = Heighest common factor

N₁ = first number, N₂ = second number

Calculation:

According to the question,

N₁ = 45

LCM = 6 HCF

LCM + HCF = 315

⇒ 6 × HCF + HCF = 315

⇒ 7 HCF = 315

⇒ HCF = 315/7

⇒ HCF = 45

⇒ LCM = 6 × HCF

⇒ LCM = 6 × 45 = 270

Then,

LCM × HCF = N₁ × N₂

⇒ 270 × 45 = 45 × N₂

⇒ N₂ = 270

∴ The other number is 270.

Discussion

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