Question

The LCM of two numbers is 28 times of their
HCF. The sum of their LCM and HCF is 1740.
If one number is 240 then what is the other
number?
A 420
B. 460
C.500
D.380​

Answer 1

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).

Answer 2

✯ Given :-

• The LCM of two numbers is 28 times of their HCF.
• The sum of their LCM and HCF is 1740.
• One number is 240.

✯ To Find :-

• What is the other number.

✯ Solution :-

LCM = 28 HCF

➣ According to the question,

⇒ LCM + HCF = 1740

⇒ 28 HCF + HCF = 1740

⇒ 29 HCF = 1740

⇒ HCF = $\sf\dfrac{\cancel{1740}}{\cancel{29}}$

➥ HCF = 60

Hence, the value of LCM = 28 × 60 = 1680

➛ One number is 240.

We know that,

$\boxed{\bold{\small{❖\: Other\: number\: =\: \dfrac{HCF\: × LCM}{One\: Number}}}}$

Now,

⇒ $\dfrac{16 × 1680}{240}$

⇒ 420

Therefore, the other number is 420. ✔ (Option a is the correct options)

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