Practice Test Discussion

LCM of two numbers is 28 times their HCF. The sum of HCF and LCM is 1740. If one of these numbers is 240, the sum of digits of the other number is

[United India Insurance (AAO) , 2012]

None of the above

Explanation

Let LCM of the two numbers= x

Then, HCF of the two numbers= $\frac{x}{28}$

Now,

$\Rightarrow x + \frac{x}{28} = 1740 \Rightarrow \frac{29 x}{28} = 1740 \Rightarrow x = \frac{1740 \times 28}{29} = 1680$

So, LCM of these two numbers =1680

Again, 240×y=1680×60

[First number × Second number]= [LCM×HCF]

or y=7×60y=420.

Hence, the number is 420 or sum of digits =4+2+0=6.

Hence, Option C is correct.

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