A radio station is having a promotion in which every 12th caller receives a free concert ticket and every 15th caller receives a limo ride. Which caller will be the first one to win both?
To do this, you find the LCM of 12 and 15.
12: 12, 24, 36, 48, 60, 72...
15: 15, 30, 45, 60, 75...
As you can see, their LCM is 60.
In conclusion, the 60th caller will receive both.
3*2*2
and
3*5
to get least common multiple first one needs 5
and second one needs 2*2 = 4
3*2*2*5 = 60
3*5 *4 = 60
After the 59th caller, make sure to be next.
Like minds think alike :)
To find the first caller who will win both the free concert ticket and the limo ride, we need to determine the least common multiple (LCM) of 12 and 15. The LCM is the smallest number that is evenly divisible by both 12 and 15.
To find the LCM of 12 and 15, you can use various methods such as prime factorization or the divisibility test. Here, I will use the prime factorization method:
Step 1: Prime factorize the two numbers:
12 = 2^2 * 3
15 = 3 * 5
Step 2: Write down the prime factors of both numbers.
12: 2^2 * 3
15: 3 * 5
Step 3: Multiply the highest powers of all prime factors:
2^2 * 3 * 5 = 60
Therefore, the LCM of 12 and 15 is 60.
Now, we know that for every 60 callers, there will be one caller who wins both the free concert ticket and the limo ride. Therefore, the caller who will be the first one to win both will be the 60th caller.
Note: This assumes that the promotion runs continuously without any interruptions or skipped calls, and there are no additional promotions or special rules in place.