(a) Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers.

\[\begin{aligned} & 18180=2^{2} \times 3^{2} \times 5 \times 101 \\ & 7575=3 \times 5^{2} \times 101 \\ & L C M=2^{2} \times 3^{2} \times 5^{2} \times 101=90900 \\ & H C F=3 \times 5 \times 101=1515 \end{aligned} \]

LCM of $\displaystyle 6$, $\displaystyle 12$, $\displaystyle 18$ = $\displaystyle 36$

So, all the three bells ring together after $\displaystyle 36$ minutes at $\displaystyle 6$ : $\displaystyle 36$ AM