Vivian has some sweets. If she shares the sweets among 4 friends, she will have 3 sweets left. If she shares the sweets among 5 friends, she will have 4 sweets left. If she shares the sweets among 9 friends, she will have 8 sweets left. What is the smallest possible number of sweets she has?
Solution:
Remember Vivian shares with friends, so the number of children in the calculation is always +1.
E.g Vivian shares with 4 friends --> number of children = 4 + 1 = 5.
Method 1: Guess and Check (as taught in Primary 3)
x5: 5, 10, 15, 20, 25, 30, 35
+3: 8, 13, 18, 23, 28, 33, 38
x6: 6, 12, 18, 24, 30, 36, 42
+4: 10, 16, 22, 28, 34, 40, 46
x10: 10, 20, 30, 40, 50, 60, 70
+8: 18, 28, 38, 48, 58, 68, 78
Check the common multiplication there: 28, 58, ...
Method 2:
Two steps:
1. Find the LCM of 5, 6, 10 , which is 30.
2. Find multiple of 5, 6, or 10, which is less than 30. For example for 5:
5 --> 5 x 5 = 25 --> 25 + 3 = 28
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