120 apples, 240 oranges and 150 pears are packed in cartons in such a way that each carton has the same number of fruits, each carton contains only one type of fruit, and no fruit is left unpacked. What is the smallest possible number of cartons needed for the purpose?

120 apples, 240 oranges and 150 pears are packed in cartons in such a way that each carton has the same number of fruits, each carton contains only one type of fruit, and no fruit is left unpacked.

120 = $$2\times2\times\ 2\times\ 3\times\ 5$$

240 = $$2\times2\times2\times\ 2\times\ 3\times\ 5$$

150 = $$2\times3\times5\times5$$

So the HCF of 120, 240 and 150 = $$2\times\ 3\times\ 5$$ = 30

Smallest possible number of cartons needed for the purpose = $$\frac{120}{30}+\frac{240}{30}+\frac{150}{30}$$

= $$4+8+5$$

= 17