Find the 4-digit smallest number which when divided by 12, 15, 25, 30 leaves no remainder?a)1020b)1120c)1200d)1800e)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

1200

Answer

Take the L.CM of -12,15,25,30
L.C.M=2*3*5*2*5=300
Therefore, four digit smallest number=300*4
=1200

Answer

LCM of 12, 15, 25 and 30 is 300
least number of 4-digit divided by 300 is 1200

Answer

The given question asks us to find the smallest 4-digit number that is divisible by 12, 15, 25, and 30 without leaving any remainder.

To solve this problem, we need to find the least common multiple (LCM) of the given numbers. The LCM is the smallest number that is divisible by all the given numbers.

To find the LCM, we can use the prime factorization method. Let's find the prime factors of each number:

12 = 2^2 * 3
15 = 3 * 5
25 = 5^2
30 = 2 * 3 * 5

Now, we need to take the highest power of each prime factor that appears in any of the numbers. So the LCM will be:

LCM = 2^2 * 3 * 5^2 = 4 * 3 * 25 = 300

Since we need a 4-digit number, we need to find the smallest multiple of 300 that is greater than or equal to 1000.

To do this, we divide 1000 by 300 and take the ceiling value to get the smallest whole number greater than or equal to the result:

1000 / 300 ≈ 3.33
⌈3.33⌉ = 4

So, the smallest multiple of 300 that is greater than or equal to 1000 is 4 * 300 = 1200.

Therefore, the 4-digit smallest number that is divisible by 12, 15, 25, and 30 without leaving any remainder is 1200, which corresponds to option C.

Answer

LCM of 12, 15, 25 and 30 is 300
least number of 4-digit divided by 300 is 1200

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