Question

Assertion (A) : For two prime numbers x and y (x < y), HCF(x, y) = x and LCM(x, y) = y. Reason (R) : HCF(x, y) ≤ LCM(x, y), where x, y are any two natural numbers.

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 √3 is an irrational number.