Question

find the smallest number which leaves 4 as remainder when divided by 44,55 ,66.​

Answer 1

Answer:

The smallest number which leaves the remainder 4 when divided by 44,55, and 66 is 664

Step-by-step explanation:

First, we shall find the smallest number that is divisible by 44, 55, and 66.

This number is called the least common multiple (LCM) of 44,55, and 66.

Then the required number is obtained by adding 4 to the LCM. The LCM can be found using the prime factorization of the given numbers. The prime factorization of the numbers are given by,

$44= 2^2\times 11\\55 = 5\times 11\\66 = 3\times 2\times 11$

Then the least common multiple is,

$LCM(44,55,66)= 2^2\times 5\times 3\times 11 = 660$

We shall now add 4 to it.

$4+660=664$

Hence 664 is the smallest number which leaves the remainder 4 when divided by 44,55, and 66.