Question

The LCM of three different numbers is 150. Which of the following cannot be their HCF?
A. 15
B. 25
C. 50
D. 55

Answer 1

Hint: LCM is the least common multiple and HCF, also called GCD, is the highest common factor. LCM is a multiple of the numbers and HCF is a factor or divisor of the numbers. This means LCM must be a multiple of HCF too, because HCF divides the given numbers. Given that the LCM of three numbers is 150. So HCF must divide 150 (LCM). Find the number from the options which does not divide 150 and that will be our answer.

Complete step by step solution:
We are given that LCM of three different numbers is 150.
We have to find a number which cannot be their HCF from the given options.
So first we have 15. 15 can divide 150 as $ 15 \times 10 = 150,\dfrac{{150}}{{15}} = 10 $ . 150 is a multiple of 15. So it can be the HCF.
Second, we have 25. 25 can divide 150 as $ 25 \times 6 = 150,\dfrac{{150}}{{25}} = 6 $ . 150 is a multiple of 25. So it can be the HCF of the given numbers.
Third, we have 50. 50 can divide 150 as $ 50 \times 3 = 150,\dfrac{{150}}{{50}} = 3 $ . 150 is a multiple of 50. So it can be the HCF of the given numbers.
Lastly we have 55. 150 is not a multiple of 55 thus 55 cannot divide 150. Therefore, 55 cannot be the HCf when LCM is 150.
So, the correct answer is “Option D”.

Note: LCM is the least common multiple and GCD (HCF) is the greatest common divisor. LCM is a common multiple of the numbers and GCD is the common divisor of the numbers. GCD is always less than or equal to LCM. GCD can also be calculated using prime factorization. Do not confuse LCM with GCD. When there are 2 given numbers, then the product of LCM and GCD is equal to the product of the numbers. It is applicable only for 2 numbers, so not for this question.