Question

Your local radio station is having their yearly music player and concert ticket giveaway. For one minute every $5^{th}$ caller will win a music player and every $7^{th}$ caller will win concert tickets. You were just the first caller to win both the music player and the concert tickets! What number caller were you?

Answer 1

Hint: According to the question given in the question we have to find the number caller i was when my local radio station is having their yearly music player and concert ticket giveaway. For one minute every $5^{th}$ caller will win a music player and every $7^{th}$ caller will win concert tickets. I was just the first caller to win both the music player and the concert tickets! So, as given in the question $5^{th}$ caller will win a music player and every $7^{th}$ caller will win concert tickets so we have to find the multiplications of 5 and 7 and then we have to consider the first number of the multiplication obtained.

Complete step-by-step answer:
In the question it is given that the same person has won both the music player and a concert ticket and it is also given that he is the first person to receive both the gifts.
From this information we can say that the lcm of both the caller number will be the answer because the least common multiple is the smallest number which is divisible by both the numbers.
We are finding the smallest number because in the question it is given that the person was the first one to receive both the prizes.
Since $5$ and $7$ are prime numbers, lcm of these two numbers will be the multiplication of the two numbers.
Multiplication of numbers 5 and 7 are $ = 35$

Hence, I am the $35^{th}$ caller.

Note: To obtain the number there is only one way which is the multiplication of the given numbers for the given conditions.
It is basically for this type of conditions or questions generally we have to find the L.C.M of the given numbers.
L.C.M stands for least common multiple and H.C.F stands for highest common factor.