Question

if the hcf of 2 numbers 180 and 420 and a natural number k is 12 and the lcm is 2^3 x 3^2 x 5 x 7, then the value of k is

Answer 1

Answer:

if the hcf of 2 numbers 180 and 420 and a natural number k is 12 and the lcm is 2^3 x 3^2 x 5 x 7, then the value of k is 18

Answer 2

Answer:

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Step-by-step explanation:

divides all the numbers i.e, HCF is common to all the numbers. <br> So, N should be a multiple

so

must be in any of the 3 number necessarily. <br> So, it is only N which will contain

. <br> Also, LCM contains 5 which will necessarily be in8 any of the 3 numbers. So, it is only N which will contain 5. Since LCM contains 103 and 2472 contains it so no need to having it in N. Similarly LCM contains 107 and it is in 1284. So, no need to having it in N....(2) <br> So, from above (1) and (2) cases of HCF and LCM , we are sure that <br>

<br> Note <br> Although N can also be

i.e., 18540,19260 and 1983780 <br> Caution: <br> Some students solve this question as, <br> Product of numbers= Product of theri LCM and HCF <br>

<br>

<br> This method (also the answer) is WRONG because formula used in this method is applicable only for two numbers.

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