which of the following represent the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12 14 21 33 and 54
Answers
Answer:
9383
Step-by-step explanation:
16)Which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54. Answer = 8316*2 - 7249 = 9383..!!
The largest 4-digit number which can be added to 7249 to make the derived number divisible by each of 12, 14, 21, 33, and 54 is 9383.
Given: The numbers 12, 14, 21, 33, and 54.
To Find: The largest 4-digit number can be added to 7249 to make the derived number divisible by each of 12, 14, 21, 33, and 54.
Solution:
- We need the largest number, so we shall focus on finding the LCM of the given values.
- The LCM can be found by the prime factorization method or the long division method. Here, we shall use the prime factorization method.
The given values are: 12, 14, 21, 33, and 54
So, we shall list down the prime factors of each of the values;
12 = 2 × 2 × 3
14 = 2 × 7
21 = 3 × 7
33 = 3 × 11
54 = 2 × 3 × 3 × 3
So, LCM ( 12, 14, 21, 33, 54 ) = 2 × 2 × 3 × 3 × 3 × 7 × 11
= 8316
Now, we have found the largest 4-digit number which can divide by 12, 14, 21, 33, and 54 which is 8316.
- But the question asks us to find the largest 4-digit number which can be added to 7249 to make the derived number divisible by each of 12, 14, 21, 33, and 54.
- So, we can subtract 7249 from the LCM to get the number to be added. But that would be a 3-digit number. So, to find the 4-digit number, we shall double the LCM and then subtract 7249 from it.
So, the required value is = ( 2 × 8316 ) - 7249
= 16632 - 7249
= 9383
Hence, the largest 4-digit number which can be added to 7249 to make the derived number divisible by each of 12, 14, 21, 33, and 54 is 9383.
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