Question

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 $?$

Answer 1

Restaurant gave every $8$^th customer a free drink,

Restaurant gave every ${12}^{th}$ customer a free snack

Restaurant gave every ${15}^{th}$ 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, ${120}^{th}$ customer will receive all the three items.

Second customer to receive all the three items will be $120\times 2$$={240}^{th}$ customer

Third customer to receive all the three items will be $120\times 3$=${360}^{th}$ customer

Hence, total $3$ customers will receive all the three items out of $385$ customers.