LCM & HCF Practice Set For MBA

Explanation
The greatest number that can divide 43, 91, and 183 and leave the same remainder in each case is 4. This means that when we divide each of these numbers by 4, the remainder will be the same. In this case, the remainder will be 3.

Explanation
The bells toll together at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively. To find out how many times they toll together in 30 minutes, we need to calculate the least common multiple (LCM) of these intervals. The LCM of 2, 4, 6, 8, 10, and 12 is 120 seconds. Since there are 60 seconds in a minute, the bells toll together every 2 minutes. In 30 minutes, they toll together 30/2 = 15 times. However, since they also toll together at the start, the total number of times they toll together in 30 minutes is 15 + 1 = 16.

Explanation
To find the HCF (Highest Common Factor) of the given numbers, we need to find the highest common factor of their prime factors. The prime factorization of the three numbers are as follows: 4 x 27 x 3125 = 2^2 x 3^3 x 5^5, 8 x 9 x 25 x 7 = 2^3 x 3^2 x 5^2 x 7, and 16 x 81 x 5 x 11 x 49 = 2^4 x 3^4 x 5 x 11 x 7^2. Now, we can see that the highest common factor of these prime factors is 2^2 x 3^2 x 5 = 180. Therefore, the correct answer is 180.

Explanation
The greatest number of three digits that leaves a remainder of 3 when divided by 6, 9, and 12 can be found by finding the least common multiple of these three numbers and subtracting 3. The least common multiple of 6, 9, and 12 is 36. Subtracting 3 from 36 gives us 33. However, 33 is a two-digit number, so we need to find the largest three-digit number that is divisible by 36. The largest three-digit number divisible by 36 is 972. However, this number does not leave a remainder of 3 when divided by 6, 9, and 12. Therefore, the correct answer is 975, which is the largest three-digit number that satisfies the given conditions.

Explanation
To find the greatest number of four digits that is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers. The LCM of 15, 25, 40, and 75 is 600. To find the greatest number of four digits that is divisible by 600, we need to find the largest multiple of 600 that is less than 10000. The largest multiple of 600 less than 10000 is 9600. Therefore, the correct answer is 9600.