The LCM of two numbers is 120. Which of the following cannot be the HCF of these numbers?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 35
The HCF divides both numbers, and the LCM is a multiple of both numbers, so the HCF must always divide the LCM.
\(120\div8=15\), so 8 can be the HCF (for example, 8 and 120)
\(120\div12=10\), so 12 can be the HCF (for example, 12 and 120)
\(120\div24=5\), so 24 can be the HCF (for example, 24 and 120)
\(120\div35\) is not a whole number, since 35 has the factor 7 and 120 does not
So 35 cannot be the HCF.