Hi there!

For the first part of first question, your answer is correct. Finding HCF is the correct method.

However, you might wish to consider writing out your numbers as a product of prime factors (which is both neater and easier to visualize).

1155: 3 × 5 × 7 × 11
462: 2 × 3 × 7 × 11
693: 3^2 × 7 × 11

HCF = 3 × 7 × 11 = 231


For the second question, now you wanna find the LCM instead (for when the security guards meet again).

Similarly, write the values out in product of prime factors as such:

A (24): 2^3 × 3
B (36): 2^2 × 3^2
C (60): 2^2 × 3 × 5

LCM (take all factors and all largest ones) =
2^3 × 3^2 × 5 = 360 or 5hours

Cheers!