During its grand opening weekend, a restaurant gave every eight customer a free drink, every twelfth customer a free snack and every fifteenth customer a free scoop of ice cream.
If $385$ customers walked into the restaurant that weekend, how many of them received all three free items $?$

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Solution

Restaurant gave every $8$ ^th customer a free drink,
Restaurant gave every $12^{t h}$ customer a free snack
Restaurant gave every $15^{t h}$ customer a free scoop of ice cream.
First customer to receive all the three items is L.C.M of $8, 12, 15$
L.C.M of $8, 12, 15$
Factors of $8 = 2^{3}$
Factors of $12 = 2^{2} \times 3$
Factors of $15 = 3 \times 5$
LCM is $2^{3} \times 3 \times 5$ = $120$ ,
Hence, $120^{t h}$ customer will receive all the three items.
Second customer to receive all the three items will be $120 \times 2$ $= 240^{t h}$ customer
Third customer to receive all the three items will be $120 \times 3$ = $360^{t h}$ customer
Hence, total $3$ customers will receive all the three items out of $385$ customers.

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During its grand opening weekend, a restaurant gave every eight customer a free drink, every twelfth customer a free snack and every fifteenth customer a free scoop of ice cream. If 385customers walked into the restaurant that weekend, how many of them received all three free items ?

During its grand opening weekend, a restaurant gave every eight customer a free drink, every twelfth customer a free snack and every fifteenth customer a free scoop of ice cream.
If $385$ customers walked into the restaurant that weekend, how many of them received all three free items $?$