Shortcut of LCM and HCF

Shortcut 82:
Maximum number of items per group
    Take HCF
Question:
There are 40, 45 and 50 balls in three different colors. They have to be arranged in boxes such that all the boxes will have equal number of balls and same colored balls. What is the maximum number of balls that can be arranged in each box?
Answer:
Take HCF of 10,45, 50
HCF = 5
5 balls per box can be arranged in the above condition.

Shortcut 83:
Minimum number of groups
Total/HCF
Question:
There are 40, 45 and 50 balls in three different colors. They have to be arranged in boxes such that all the boxes will have equal number of balls and same colored balls. What is the minimum number of boxes required?
Answer:
HCF = 5
Total number of balls = 40 + 45 + 50 = 135
Minimum number of boxes required = 135/5 = 27

Shortcut 84:
Ringing Bells
     Take LCM
Question:
There are three different bells. The first bell rings every 4 hour, the second bell rings every 6 hours and the third bell rings every 15 hours. If all the three bells are rung at same time, how long will it take for them to ring together?
Answer:
Take LCM of 4, 6, 15
LCM (4,6,15) = 60
All the three bells will ring after 60 hours

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