The product of three numbers is 1620. If the HCF of any two out of the three numbers is 3, what is their LCM?
One day the king summoned all the soldiers in his army and made them stand in a queue. To the first soldier, he gave three gold coins and to every subsequent soldier, he gave four gold coins more than what he gave to the previous soldier. Then the king ordered each soldier to distribute all the coins that he received among the peasants, if and only if it is possible to distribute the coins such that each peasant to whom the soldier distributes gets as many coins as the number of peasants to whom the soldier distributes the coins. If no two soldiers were allowed to distribute coins to the same peasant and there were a total of 4000 soldiers in the king's army, how many peasants received at least one gold coin?
Anoop found the product, P, of two two-digit natural numbers, M
and N. He then reversed the digits of each of M and N and found the
product of the resultant numbers. Interestingly, he found both
products to be the same. If the product of the tens digit of M and the
tens digit of N is prime, find the sum of all the possible values of P
that Anoop could have obtained.