Question

A boy was asked to find the LCM of 3,5,12 and another number.But while calculating,he wrote 21 instead of 12 and yet came with the correct answer.what could be the fourth number?

Answer 1

original figures:
LCM of 3,5 and 12= 3 x 5 x 4 =60

Mistakenly wrong figure:
LCM of 3,5 and 21 = 3 x 5 x 7 =105

fourth number = x
when X is included in both figure the answer gets the same.

So x must be a product of the numbers which are not common in the list of factors. So that these numbers can be a part of the final multiple.

difference of both LCM = 28
the fourth number = x=4 x 7=28

Now
 LCM of 3,5,12,28 =  3x 4 x 5 x 7=420
LCM of 3,5,21,28 =  3 x 7 x 5 x 4 =420

Answer 2

Solution:-
Let the fourth number be 'a'
Suppose LCM of 3, 5, 12 and a = x
And LCM of 3, 5, 21, and a = y
Using prime factorization,
12 = 2 × 2 × 3
21 = 3 × 7
Given : x = y
So, a should contain the factors 2 × 2 ×7
Thus, a = 2 × 2 × 7 = 28
Again using prime factorization,
3 = 3
5 = 5
12 = 2 × 2 × 3
21 = 3 × 7
28 = 2 × 2 × 7
So, L. C. M. of 3, 5, 12, and 28 = 3 × 5 × 2 × 2 × 7 = 420
L. C. M. of 3, 5, 21 and  28 = 3 × 5 × 2 × 2 × 7 = 420
So, the fourth number is 28
Answer.