A, b, c are positive integers. a:b = 3:8 b:c = 6:11 work out the smallest possible value of a+b+c

Work out the a:b:c ratio.

b is present in both ratios, find first the LCM of 8 and 6, which is 24.

Multiply a:b=3:8 by 3 to get a:b=9:24

Similarly, multiply b:c=6:11 by 4 to get b:c=24:44

Then we conclude

a:b:c=9:24:44

Since there is no common factor among the three numbers, this is the simplest ratio possible.

If a, b and c are integers, the smallest values for a, b and c are 9,24,44.

Add up the three numbers to get the least value of a+b+c.