Multiple choice

The HCF of two numbers is 12. Which one of the following can never be their LCM?

  1. 72

  2. 60

  3. 90

  4. 84
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If HCF of two numbers is 12, then both numbers are multiples of 12. Let the numbers be 12a and 12b where a and b are coprime. Their LCM = 12ab must be a multiple of 12. Checking the options: 72 = 12×6 (multiple of 12, possible), 60 = 12×5 (multiple of 12, possible), 84 = 12×7 (multiple of 12, possible), but 90 = 12×7.5 (not an integer multiple of 12, so 90 cannot be the LCM). The LCM must always be divisible by the HCF.

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