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Method of Finding LCM

Six bells com...

Question

Six bells commence tolling together and toll at intervals of $2, 4, 6, 8, 10$ and $12$ seconds each. After how much time will they toll together again?

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Solution

$L C M o f 2, 4, 6, 8, 10 a n d 12 i s 120.$

$S o, a f t e r e a c h 120 s e c o n d s, t h e y w o u l d t o l l t o g e t h e r .$

$H e n c e, i n 30 m i n u t e s, t h e y w o u l d t o l l \frac{30 \times 60 s e c o n d s}{120 s e c o n d s} = 15 t i m e s$

$B u t t h e n t h e q u e s t i o n s a y s t h e y c o m m e n c e t o l l i n g t o g e t h e r . S o, t h e y b a s i c a l l y a l s o t o l l a t t h e " b e g i n n i n g " (" 0 " s e c o n d) .$

$S o, t o t a l t o l l s t o g e t h e r = 15 + 1 = 16$

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