Question

The LCM of two numbers is 40 times of the HCF the sum of the LCM and HCF is 1476 if one of the numbers 288 then other number is

Answer 1

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Answer 2

The other number is 180

Solution:

We know that,

$\mathrm{LCM} \times \mathrm{HCF} =$ Product of two numbers

$L C M=40 \times H C F \ldots \ldots \ldots(1)$

LCM + HCF = 1476

40 HCF + HCF = 1476

41 HCF = 1476

$H C F=\frac{1476}{41}$

HCF = 36………..(2)

By substuting 2 in 1, this results in,

$L C M=40 \times 36$

LCM= 1440………(3)

As we known that if product of two numbers A and B let say, such that  

$A \times B=LCM \times HCF$

$A \times B=1440 \times 36$

From the given, that one of the two numbers in A and B is 288, so we can taken B as 288.

$A \times 288=1440 \times 36$

Such that value of $A = 1440 \times \frac{36}{288}$

= 180

Therefore, the other number is 180