A boy was asked to find the L.C.M. 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?

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answer is A.

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Detailed Solution

Concept-Now we need to figure out what the fourth number is. The fourth number is X. First, write down the given number as a product of prime factors. Then use the prime number product to observe the greatest powers of the prime factors of 3, 5 and 12 and the greatest powers of the prime factors of 3, 5 and 21. The L.C.M. is the same in both cases, but the prime factor with the largest power must be the same in both cases. Compare the highest power prime factors of 3, 5, and 12 with the highest power prime factors of 3, 5, and 21. Find the fourth number by multiplying the factors that are not common to both cases.
The fourth digit is 'a'
Suppose the LCMs are 3, 5, 12 and a=x.
and LCM for 3, 5, 21 and a=y
In prime factorization,

Given: x = y
So a must contain factors of

Therefore, a=2×2×7=28
By prime factorization again,
Question Image

So 3, 5, 12, and 28 LCMs

So. the fourth number is 28
Hence the correct option is 1.

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