adkikani wrote:

niks18 BunuelVeritasPrepKarishma**Quote:**

Let's assume that \(S = p_1^a*p_2^b\) where \(p_1\) & \(p_2\) are some prime nos

and \(T=p_1*p_3\), where \(p_1\) & \(p_3\) are prime nos

Can you explain why is there a difference in notation for S and T, meaning how did

you assume \(T=p_1*p_3\)

For all I know, S and T can very well be two distinct prime numbers.

Should not T be expressed as \(T=p_3^x*p_4^y\)

The basic definition of LCM and GCF comes as follows:

a. For LCM, we break down a no in to its prime factors and list highest powers

of ALL prime factors.

b. For HCF, we list for least power of common prime factors.

I picked up completely opposite answer here ie B instead of A with my above understanding.

Hi

adkikani,

you can assume any prime factor for either of the numbers but as you have mentioned the process for calculating LCM & HCF, use it to find LCM, HCF & the product.

So let's take your example for \(T\)

\(S = p_1^a*p_2^b\)

\(T=p_3^x*p_4^y\)

LCM of \(S\) & \(T=p_1^a*p_2^b*p_3^x*p_4^y\)

HCF of \(S\) & \(T=1\) as no prime factors are common

Product of \(S\) & \(T=p_1^a*p_2^b*p_3^x*p_4^y\)

Now you can see that all prime factors in the LCM are there in the product of these two numbers.

you can take any other example for S & T or may be assume simple numbers for S & T to arrive at the answer.

Point is the definition of LCM clearly states that it is the LEAST COMMON MULTIPLE of all the prime factors of the given number and when you multiple those given numbers it will automatically contain the prime factors of the numbers.