Question

The LCM of two numbers is 28 times of their HCF.The sum of their LCM and HCF is 1740.lf one
number is 240 then what is the other number?
(a) 420 (b) 460 (c) 500 (d) 380

Answer 1

Answer:

420

Step-by-step explanation:

LCM=28 x HCF

LCM+HCF=1740

28HCF+HCF=1740

29HCF=1740

HCF=60

LCM x HCF= product of two numbers

28HCF x HCF= 240 x other number

28 x 60 x 60 = 240 x other number

other number = 420

Answer 2

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Answer:-

Given:

LCM of two numbers is 28 times of their HCF.

⟶ LCM = 28HCF -- equation (1)

Sum of their LCM and HCF = 1740

⟶ LCM + HCF = 1740

⟶ 28HCF + HCF = 1740

[ From equation (1) ]

⟶ 29HCF = 1740

⟶ HCF = 1740/29

⟶ HCF = 60

Substitute the value of HCF in equation (1).

⟶ LCM = 28(60)

⟶ LCM = 1680

Also given that,

One of the numbers = 240.

So, Let the other number be x.

We know that,

Product of two numbers = HCF × LCM

⟶ (240)(x) = (60)(1680)

⟶ x = (60)(1680) / 240

⟶ x = 420

∴ The other number is 420 (Option - A).