Question

Assertion (A) : For two odd prime numbers x and y, (x ≠ y), LCM(2x, 4y) = 4xy Reason (R) : LCM(x, y) is a multiple of HCF(x, y).

Let p = x² y³ zⁿ and q = x³ yᵐ z², where x, y, z are prime numbers. If LCM (p, q) = x³ y⁴ z³, then the value of (2m + 3n) is

Prove that √2 is an irrational number.

Let x and y be two distinct prime numbers and p = x²y³, q = xy⁴, r = x⁵y². Find the HCF and LCM of p, q and r. Further check if HCF (p, q, r) × LCM (p, q, r) = p × q × r or not.