Question: The LCM of three different numbers is 150. Which of the following can't be their HCF?
To find the Least Common Multiple (LCM) of two numbers, we need the least number which is exactly divisible by both the numbers without leaving any remainder.
Answer: (d) 55
LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.
LCM of three numbers is the multiple of their HCF.
Therefore, the HCF of three numbers completely divides their LCM without leaving any remainder.
Now among all the four numbers 15, 25, 50, and 55 all the numbers completely divide 150 except 55.
Therefore 55 can't be the HCF of those three numbers.
Therefore, option (d) 55 is the correct option.