Question

If two positive integers are expressible in the form = 3 and =

3

2

,

Where , are prime numbers, then find H.C.F (, ) and LCM (m,n). What do you

observe?​

Answer 1

Answer:

The HCF of any two number a and b is the highest common factor that divides both number a and b.

Given : Two positive integers m and n are expressible in the form of m=pq^3m=pq3 and  n=p^3q^2n=p3q2 , where p,q are prime numbers.

Prime Factorization of m = p \times q\times q\times qp×q×q×q  [∵p,q are prime numbers]

Prime Factorization of n = p \times p\times p\times q\times qp×p×p×q×q [∵p,q are prime numbers]

Highest common factor of m and n : HCF (m,n)= p \times q\times q = pq^2p×q×q=pq2

Hence, the HCF(m,n)= pq².

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