A boy was asked to find the LCM of 3, 5 and 12 and anotger number. But while calculating, he wrote 21 instead of 12 and yet came with the correct answer. What could be the fourth number?
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Step-by-step explanation:
The prime factors of 3, 5, 12 are 3, 4, 5
and the prime factors for 3, 5, 21 are 3, 5, 7
In order for the LCM to be the same the prime factors have to be the same. but in the first case 7 is missing and in the second case 4 is missing. So, the answer should be a product of these two numbers ie 28.
Now, with 28, the prime factors for 3, 5, 12, 28 are 3, 4, 5, 7 and the LCM will be 3 * 4* 5 * 7 = 420
and as with 21 the prime factors for 3, 5, 21, 28 are 3, 4, 5, 7 and the LCM again is 3 *4 * 5* 7 = 420
Hence 28 is the answer.
Note: There are many answers to the question and 28 is the smallest possible number and all the multiples of 28 are possible solutions for this question.
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