Question

I am a multiple of 3,4,5 and 6. I am a factor of 120. Divided by 7, i leave a remainder of 4. Who am i?

Answer 1

I am a multiple of 3,4,5 and 6. I am a factor of 120. Divided by 7, I leave a remainder of 4. I am 60.

Given:

Multiple of 3,4,5 and 6.

The factor of 120.

When divided by 7, it leaves a remainder of 4.

To Find:

The original number.

Solution :

Least Common Multiple of 3,4,5 and 6

$\begin{array}{r | l} 2 & 3, 4, 5, 6 \\ \cline{2-2} 2 & 3, 2, 5, 3 \\ \cline{2-2} 3 & 3, 1, 5, 3 \\ \cline{2-2} 5 &1, 1, 5, 1 \\ \cline{2-2} & 1, 1, 1, 1 \end{array}$

=> 2 x 2 x 3 x 5 = 60

60 is a multiple of 3,4,5, and 6.

=> 3 x 20 = 60

=> 4 x 15 = 60

=> 5 x 12 = 60

=> 6 x 10 = 60

60 is also a factor of 120.

Factors of 120 =  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. 

when 60 is divided by 7, it gives a remainder of 4.

7) 60 ( 8

- 56

_____

4

_____

Hence, The required answer is 60.