LCM of two numbers is 180. Which of the following is not the HCF of the numbers?
45
60
75
90
Idea:
The HCF (highest common factor) of two numbers divides each number.
So the HCF must also divide every common multiple of the two numbers.
The LCM is the least common multiple, so the HCF must divide the LCM.
Given: LCM = 180. Therefore, a possible HCF must be a factor of 180.
Check each option by dividing 180:
\(180 \div 45 = 4\) → whole number ✔
\(180 \div 60 = 3\) → whole number ✔
\(180 \div 75 = 2.4\) → not a whole number ✖
\(180 \div 90 = 2\) → whole number ✔
Only 75 does not divide 180 exactly, so it cannot be the HCF.
Answer: C) 75