The Least Common Multiple of three different numbers is 120. Which of the following cannot be their Highest Common Factor?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 16.
Prime Factorization of 120
⇒ 120 = 23 × 3 × 5
The divisors of 120 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
15 = 3 × 5
This is a divisor of 120, so it is possible for the HCF of three numbers with LCM 120 to be 15.
40 = 23 × 5
This is also a divisor of 120, so the HCF of three numbers with LCM 120 can be 40.
20 = 22 × 5
This is a divisor of 120, so the HCF of three numbers with LCM 120 can be 20.
16 = 24
This is not a divisor of 120, because 120 only has (23) as its highest power of 2.
Hence the HCF of three numbers with LCM 120 cannot be 16, since 16 is not a divisor of 120.