Three company of
soldiers containing 120, 192, and 144 soldiers are to be broken down into
smaller groups such that each group contains soldiers from one company only and
all the groups have equal number of soldiers. What is the least number of total
groups formed?
Which one to go LCM or HCF??
From the problem, it is clearly mentioned least number of total groups. Total groups can be least only when the soldiers in each group are more. Also we should make sure each group to have equal number of soldiers from one company only. To satisfy both the statements above we have to find the largest group that is common to all the 3 companies. So we will go for HCF of 120, 192 and 144.
HCF of 120, 192 and 144 is 24.
How to do HCF of 120,192,144?
Lets do HCF with Division Method:
Get the largest and smallest number from the given list which is 192 and 120.
192 Divided by 120 leaves Remainder 72
120 Divided by 72 leaves Remainder 48
72 Divided by 48 leaves Remainder 24
48 Divided by 24 leaves Remainder 0.
Therefor 24 is the Highest common factor which divides 192,144 and 120 equally.
Now divide each group by 24 to get number of groups
120 / 24 = 5
192 / 24 = 8
144 / 24 = 6
Total number of least groups having equal soldiers from 3 companies is 5 + 8 + 6 = 19.
