Mathematics
If the LCM of two natural numbers is 180, then which of the following is not the HCF of the numbers?
45
60
75
90
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Answer
LCM of two numbers is always exactly divisible by their HCF. So the HCF must be a factor of the LCM.
180 ÷ 45 = 4 ✓ (45 is a factor)
180 ÷ 60 = 3 ✓ (60 is a factor)
180 ÷ 75 = 2.4 ✗ (75 is not a factor)
180 ÷ 90 = 2 ✓ (90 is a factor)
So 75 cannot be the HCF.
Hence, option 3 is the correct option.
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