Question

find the smallest number which when divided by 24 36 and 64 leaving 4 as remainder in each case​

Answer 1

Answer: 580

Step-by-step explanation:

LCM concept ...

LCM of 24, 36, 64 is 576 hence 580 is that number which is divisible by three  and give 4 as a reminder.

Answer 2

The smallest number when divided by 24, 36, and 64 leaving 4 as the remainder in each case is 580.

Given: The numbers 24, 36, and 64.

To Find: The smallest number when divided by 24, 36, and 64 leaves 4 as the remainder in each case.

Solution:

Since we are asked to find the smallest number, we need to find the LCM of the required numbers.

The numbers are = 24, 36, and 64

Let us find the LCM by prime factorization.

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

64 = 2 × 2 × 2 × 2 × 2 × 2

So, the LCM ( 24, 36, 64 ) = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

                                           = 576

Now, since we need to find the smallest number which when divided by 24, 36, and 64 leaves 4 as the remainder in each case​, so we need to add 4 to the LCM of the numbers.

So, the smallest number is = 576 + 4

                                            = 580

Hence, the smallest number when divided by 24, 36, and 64 leaving 4 as the remainder in each case is 580.

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