Question

7. A number m is such that when it is

dividedby 30, 36, and 45 the
remainder is always 7, find
the smallest possible value of m. (3
marks)

Answer 1

To find the smallest possible value of m, we calculate the least common multiple (LCM) of 30, 36, and 45 and add 7 to it.

Step-by-step explanation:

To find the smallest possible value of m, we can consider finding the least common multiple (LCM) of 30, 36, and 45. The LCM of these three numbers will give us the smallest number that is divisible by all three numbers. By finding the LCM, we can then add 7 to get the smallest possible value of m. Let's calculate it:

1. 30 = 2 * 3 * 5
2. 36 = 2 * 2 * 3 * 3
3. 45 = 3 * 3 * 5

Now, we take the highest power of each prime factor:

• 2^2 * 3^2 * 5 = 180

Finally, we add 7 to get the smallest possible value of m:

m = 180 + 7 = 187

Learn more about Finding the LCM of numbers