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1764 = 2x2x3x3x7x7

26460= 2x2x3x3x7x7x3x5

Since P and 1764 share 18 as HCF

P minimally must be 18 and is a multiple of 18

Notice 26460 and 1764 share almost similar prime factors (2x2x3x3x7x7) with the exception of 3x5, for 26460 to be the LCM of 1764 and P, you take HCF of both numbers (18) and multiply with the difference in prime factors between 1764 and 26460 (3x5)

Hence P=3x5x18=270

26460= 2x2x3x3x7x7x3x5

Since P and 1764 share 18 as HCF

P minimally must be 18 and is a multiple of 18

Notice 26460 and 1764 share almost similar prime factors (2x2x3x3x7x7) with the exception of 3x5, for 26460 to be the LCM of 1764 and P, you take HCF of both numbers (18) and multiply with the difference in prime factors between 1764 and 26460 (3x5)

Hence P=3x5x18=270

Thanks