Practice question · Select all that apply
Select every TRUE statement about gcd and lcm for the numbers 12 and 18.
Hints
- Compute both, then check the two general size claims against your answers.
- A divisor cannot exceed the number it divides; a multiple cannot be smaller than the number it is a multiple of.
Show the answer
- A. gcd(12, 18) = 6
- D. The gcd is never larger than the smaller of the two numbers
- E. The lcm is never smaller than the larger of the two numbers
- F. lcm(12, 18) = 36
Why
gcd(12, 18) = 6 and lcm = (12 x 18)/6 = 36. The size rules follow from the definitions: a common DIVISOR is at most the smaller number, a common MULTIPLE is at least the larger. 216 is just 12 x 18, which is only the lcm when the two are coprime.
Practise GCD and the Euclidean Algorithm
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