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The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF is 1456. If one of the number is 160, then what is the other number?

The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF is 1456. If one of the number is 160, then what is the other number? Correct Answer 144

Given:

LCM = 90 × HCF

LCM + HCF = 1456

One of the Numbers = 160

Formula Used:

Product of two numbers = Product of their LCM and HCF

Calculations:

Let HCF be x and the other number be N

⇒ LCM = 90x

The sum of LCM and HCF = 91x

⇒ 91x = 1456

⇒ x = 16

LCM × HCF = 160 × N

⇒ 90 × 16 × 16 = 160 × N

⇒ N = 144

∴ The other Number is 144

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