vikasbansal227
Dear All,
Its difficult that on what basis we took "First common integer in two patterns" as a remainder for the formula?
Can someone please explain,
Thanks
You want a number, n, that satisfies two conditions:
"leaves a remainder of 4 after division by 6" and
"a remainder of 2 after division by 8"
So you find the first such number by writing down the numbers. You get that it is 10.
10 satisfies both conditions.
What will be the next number?
Any number that is a multiple of 6 more than 10 will continue to satisfy the first condition. e.g. 16, 22, 28, 34 etc
Any number that is a multiple of 8 more than 10 will continue to satisfy the second condition. e.g. 18, 26, 34 etc
So any number that is a multiple of both 6 and 8 more than 10 will satisfy both conditions.
LCM of 6 and 8 is 24. 24 is divisible by both 6 and 8.
So any number that is a multiple of 24 more than 10 will satisfy both conditions.
e.g. 34, 58 .. etc
These numbers can be written as 10 + 24a.
Also, I think you did not check out the 4 links I gave here:
positive-integer-n-leaves-a-remainder-of-4-after-division-by-93752-40.html#p1496547They are very useful in understanding divisibility fundamentals.