Question

If p = 23 x 3, q = 2 x 3 x 5, r = 3k x 5 and LCM (p,q,r) = 23 x 32 x 5, then find the  value of k.​

Answer 1

Given :- p = 23 x 3, q = 2 x 3 x 5, r = 3k x 5 and LCM (p,q,r) = 23 x 32 x 5 .

Solution :-

→ p = 23 * 3

→ q = 2 * 3 * 5

→ r = 3k * 5

since LCM takes highest values of prime factors,

→ LCM(p , q, r) = 23 * 3k * 2 * 5

A/q,

→ 23 * 32 * 5 = 23 * 3k * 2 * 5

→ 32 = 3k * 2

→ 16 = 3k

→ k doesnt have any positive integer value .

if we assume ,

→ p = 2³ * 3

→ q = 2 * 3 * 5

→ r = 3^k * 5

→ LCM = 2³ * 3² * 5

then,

→ 2³ * 3^k * 5 = 2³ * 3² * 5

→ k = 2 .

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