Puzzle 105 - Product of lcm and gcd

-


What is the pair of numbers whose product is equal to the product of its least common multiple (LCM) and greatest common divisor (GCD)?

The GCD is the largest positive integer that divides each of two or more integers.  
The LCM is the smallest positive integer that is divisible by both integers


You can find the solution here .

Hint: The problem is much much easier than you think. 


Comments

Post a Comment

Popular posts from this blog

Puzzle 9 : The 4 coins problem

-
Image
 Solution to puzzle 8: Maria is not counting Sundays. So she is not counting 1/7th of days of her age.  That is to say she is only counting 6/7th of her age. 6/7th of her age = 30 Her actual age = 30 X 7/6 = 210/6 = 35 years.  Puzzle 9 : The 4 coins problem  You’re creating a new coin system for your country. You must use only four coin values and you must be able to create the values 1 through 10 using one coin at a minimum and two coins maximum.    What 4 coins do you choose, and can you think of a second set of 4 coins that achieves the same goal?
Read more

Puzzle 13 - Alibaba's cave

-
Solution to puzzle 12: I am using brute force algorithm here. Let us start from the divisibility of 5. If two cards remain after dealing them for 5, the largest value less than 52 will be 47 If there are 47 cards and they are dealt to 3 people, 2 cards are left If they are dealt to 4 people 47 - 44 = 3 cards are left So 47 is the correct answer. Puzzle 13 : Alibaba's cave This puzzle is from mrbartonmaths Ali Baba found a cave full of gold and diamonds. A bag full of gold weighs 200 kilograms, a bag full of diamonds weighs 40 kilograms. Ali Baba can carry only 100 kilograms at a time. A kilogram of gold costs $20, and a kilogram of diamonds costs $60. What is the greatest amount of money Ali Baba can earn for the gold and diamonds he can carry out at once (in one attempt in one bag)?
Read more

Puzzle 128 - Kings and Queens

-
Image
 On a table, 3 normal playing cards are placed face down.  To the right of a king, there is a queen or queens. To the left of a queen there is a queen or queens.  To the left of a heart, there is a spade or spades.  To the right of a spade, there is a spade or spades.  Which three cards are on the table? (Borrowed from the book "The colossal book of short puzzles and problems" by Martin Gardner)  Show answer The first rule says that there is atleast one king. Second rule says that there are two queens. (KQQ,QKQ) Third rule says that there is a heart and a spade. And the fourth rule says that there are two spades. (HSS,SHS,SSH) Which means out of three cards, two are queens and one is king. And two are spades and one is hearts. So the four possibilities are   KS, QS, QH KS, QH, QS QS, KS, QH QS, KH, QS The fourth is an impossible option as there can't be two queen of spades in a deck. So the three possible answers are  King of s...
Read more