Find the smallest possible integer when divided by either 3,4 or 5 with a remainder of 2.

Don't understand!!

We have to find the least common multiple (LCM) of 3, 4 and 5. LCM is the smallest number that when divided by 3 or 4 or 5 should give no remainder.

Their LCM is 60.
Since the problem is asking "with a remainder of 2", we just add 2 to 60, therefore it's 62.

Well, let me explain it to you in a funny way. Imagine you have three friends, let's call them Three, Four, and Five. These friends have a strange requirement for dividing numbers. They want an integer that when divided by 3, 4, or 5, it should always leave a remainder of 2.

Now, let's start counting:

2 (remainder when divided by all three friends)
5 (remainder 2 when divided by 3 and 4)
8 (remainder 2 when divided by all three friends)
11 (remainder 2 when divided by 3 and 4)
And so on...

Now, let's keep going until we find the smallest integer that fits the requirement.

To make it more exciting, let's add a drumroll... da-da-da-da!

After a long and dramatic countdown... the smallest integer that works is...

The Lilliputian number: 47!

That's right, my friend. 47 is the smallest possible integer that, when divided by 3, 4, or 5, leaves a remainder of 2.

I hope that clears it up for you in a funny way!

To find the smallest possible integer that satisfies the given condition, we can start by considering the remainders when dividing consecutive integers by 3, 4, and 5.

When dividing consecutive integers by 3, the possible remainders are: 0, 1, and 2.
When dividing consecutive integers by 4, the possible remainders are: 0, 1, 2, and 3.
When dividing consecutive integers by 5, the possible remainders are: 0, 1, 2, 3, and 4.

We are looking for an integer that leaves a remainder of 2 when divided by any of these three numbers. Therefore, we need to find the first integer that satisfies the condition of having a remainder of 2 when divided by 3, 4, and 5.

To find this integer, we can start by looking for multiples of the least common multiple (LCM) of these three numbers, which is 60.

Starting with 60, the remainders when dividing consecutive integers by 3, 4, and 5 are:
60 ÷ 3 = 20 with a remainder of 0,
60 ÷ 4 = 15 with a remainder of 0,
60 ÷ 5 = 12 with a remainder of 0.

The next possible integer that leaves a remainder of 2 when divided by 3, 4, and 5 is obtained by adding 2 to the LCM:

60 + 2 = 62.

Therefore, the smallest possible integer that satisfies the given condition is 62.

To find the smallest possible integer when divided by 3, 4, or 5 with a remainder of 2, we need to find the least common multiple (LCM) of these three numbers and then add 2 to that number.

The LCM of 3, 4, and 5 is 60. To understand this, we can find the LCM by examining the multiples of each number:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60...

We can see that the smallest number that satisfies the remainder of 2 when divided by 3 is 2, when divided by 4 is 4, and when divided by 5 is 5. The first number that satisfies all three conditions is 60.

Finally, we add 2 to the LCM (60 + 2) to get the smallest possible integer when divided by 3, 4, or 5 with a remainder of 2, which is 62.

Therefore, the smallest possible integer that meets the given conditions is 62.