Question

if two positive integers p and q can be expressed as p=ab2 and q=a2b.a and b being prime numbers then find HCF(p,q)

Answer 1

Answer:

(b) Given that, p = ab2 = a × b × b

and q = a3b = a × a × a × b

∴ LCM of p and q = LCM (ab2,a3b) = a × b × b × a × a = a3b2

[Since, LCM is the product of the greatest power of each prime factor involved in the numbers].

Answer 2

$\huge\underline\bold\red{Answer}$

$given \: that \: \: \: p = {ab}^{2} \: \: and \: q = {a}^{2} b$

We have to find the LCM of (p,q)

$p = {a} \times {b}^{2}$

$q = {a}^{2} \times b$

LCM is the product of the greatest power of each prime factor involved in the numbers .

Therefore,

$(lcm(p \: \: q) = {b}^{2} \times {a}^{2} = {a}^{2} {b}^{2}$

$thus \: \: lcm \: of \: p \: and \: q \: is \: {a}^{2} {b}^{2}$