Question

7. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7, find the smallest possible value of m. (3 marks)

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Answer 1

187

Explanation:

Least common multiple:

To find the required number,

1. Find the LCM of 30 , 36 and 45
2. Then add 7 to the LCM

30 = 2 * 3 * 5

36 = 2 * 2 * 3 * 3 = 2² * 3²

45 = 2 * 3 * 3 = 2 *3²

LCM = 2² * 3² * 5

= 4 * 9 * 5

= 180

Required number = 180 + 7

= 187