• # question_answer The two numbers nearest to 10000 which are exactly divisible by each of 2, 3, 4, 5, 6 and 7, are _________. A)  9660, 10080B)  9320, 10080C)  9660, 10060D)  10340, 10080

The numbers which are exactly divisible by 2, 3, 4, 5, 6 and 7 are the multiples of the LCM of the given numbers. $\therefore$ $\text{LCM= 2}\times \text{2}\times \text{3}\times \text{5}\times \text{7=420}$ Now, dividing 10000 by 420, we get remainder = 340 $\therefore$ Number just less than 10000 and exactly divisible by the given numbers = 10000 - 340 = 9660 Number just greater than 10000 and exactly divisible by the given numbers = 10000 + (420 - 340)=10080