On a store’s 100th anniversary, every person who enters gets a pin. Every fourth person gets a mug. Every tenth person gets perfume. Every 25th person gets an umbrella, and every 75th person gets a free dinner.
To find the shopper to get all the 5 gifts, we take LCM of 1, 4, 10, 25 and 75
Multiple of 1 : 1, 2, 3 , 4...............299, 300, 301, 302
Multiple of 4 : 4, 8, 12, 16, 20,............., 296, 300, 304........
Multiple of 10: 10, 20, 30, 40 ......................290, 300, 310.....
Multiple of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300....
Multiple of 75: 75, 150, 225, 300, .....
LCM of 1, 4, 10, 25, 75 is 300
So 300th shopper will be the first to get all 5 gifts.
