Question

The lcm of 96,144 and n is 576 if their hcf is 48 then the value of n is

Answer 1

Answer:

The required value of n is 192.      

Step-by-step explanation:

Given : The LCM of 96,144 and n is 576 if their HCF is 48.

To find : The value of n ?

Solution :  

Factors of the number are

$576 = 2 \times 2\times2\times2\times2\times2\times3\times3=2^6 \times3^2$

$96 = 2 \times 2\times2\times2\times2\times3=2^5 \times3$

$144 = 2 \times 2\times2\times2\times3\times3=2^4\times3^2$

LCM of 96,144 and n is 576.

i.e. $n=2^6\times k=64k$ ....(1)

HCF is 48.

$\text{HCF(96,144,64k)}= 2^4\times3$

$48= 2^4\times3$

This only happen if k=3

So, substituting k=3 in (1),

$n=64(3)=192$

Therefore, The required value of n is 192.