The HCF of two numbers is 21 and their LCM is 221 times the HCF. If one of the numbers lies between 300 and 360, then the square of sum of the digits of the other number is:

144

LCM = HCF × (product of other factors)

ATQ,

LCM = HCF × 221

Product of other factors = 221 = 13 × 17

Therefore,

1st no. = 13 × HCF = 13 × 21 = 273

2nd no. = 17 × HCF = 17 × 21 = 357  (lies b/w 300 and 360)

Hence,

Sum of digit of other no. i.e. 273 = 2 + 7 + 3 = 12

Square of sum of digits = 12² = 144