determine the two numbers nearest to 10000 which are exactly - Maths - Factors and Multiples

Question

determine the two numbers nearest to 10000 which are exactly
divisible by each of 2 ,3 ,4 ,5 ,6 and 7

Ankush Jain · Accepted Answer

In order to find out the two nearest numbers which are divisible by 2,3,4,5,6,7 firstly we have to find the LCM of 2,3,4,5,6,7 as: $\begin{matrix} 2 & 2, 3, 4, 5, 6, 7 \\ 2 & 1, 3, 2, 5, 3, 7 \\ 3 & 1, 3, 1, 5, 3, 7 \\ 5 & 1, 1, 1, 5, 1, 7 \\ 7 & 1, 1, 1, 1, 1, 7 \\ 1, 1, 1, 1, 1, 1 \end{matrix}$ So, LCM of 2,3,4,5,6,7 = 2 Ã— 2 Ã— 3 Ã— 5 Ã— 7 = 420 Now, the division of 10000 by 420 is carried out as:

So, on dividing 10000 by 420, we get 340 as the remainder Therefore, the number which is divisible by each of 2,3,4,5,6,7 and nearest to 10000 = 10000 - 340 = 9660 The other number which is divisible by each of 2,3,4,5,6,7 and nearest to 10000 is obtained by multiplying 420 with the number which is successor of quotient i e , 24 âˆ´ 420 Ã— 24 = 10080 Hence, the two numbers which are nearest to 10000 and are divisible by each of 2,3,4,5,6,7 are 9660 and 10080 respectively

determine the two numbers nearest to 10000 which are exactly divisible by each of 2 ,3 ,4 ,5 ,6 and 7.