What is the smallest positive integer value of n such that 63n is a multiple of 14?

Answer 1

Let's us say that the pth multiple of 14 is 63n i.e. 14p = 63n.

14p = 63n and n = 14p/63....(1)

From the relation 1 it is clear that we have to look for the multiple of 14 which is divisible by 63.

Method 1:

Let's us write the multiples of 14 greater than 63: 70, 84, 98, 112, 126, 140 etc.

Is any of these multiples a multiple of 63?

126 is the required multiple and it is the second multiple(n=2) of 63.

So the smallest value of n is 2.

Method 2:

The smallest value of n can be found by calculating the LCM of 63 and 14.

LCM of x and y gives us the smallest number divisible by x and y.

LCM of 63 and 14 is 126. And putting 63n equal to 126 gives:

63n = 126

n =2