Find the least 5 digit number which is exactly divisible by

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answer is B.

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Detailed Solution

Concept- First, we know at least five digits. Find the least common multiple (LCM) of these numbers to get the smallest number. Then multiply the LCM by a number that results in a minimum of 5 digits. First, find the divisors of the three given numbers. Then find the least common multiple of the three numbers. The problem is that LCM can be calculated by prime factorization. The procedure for this method is
(i) Make a note of all the prime factors of each number. (ii) List all prime numbers. (iii) Finally, multiply the list of prime factors
20 = 1 × 2 × 2 × 5 =

{2^{2}}^{}

× 51
25 = 1 × 5 × 5 =

5^{2}

30 = 1 × 2 × 3 × 5 =

2^{1}

3^{1}

5^{1}

Least common multiple of

The minimum 5-digit number is 10000
Dividing 10000 by 300 gives the quotient 33.33.
An integer slightly greater than 33.33 is 34.
∴ Required number = 300 × 34 = 10200
Therefore, the smallest 5-digit number that is exactly divisible by 20, 25, and 30 is 10200.
Hence, the correct option is 2.

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