Exercise · ZW-LEAST-COMMON-MULTIPLE-007 · ★★☆ Intermediate
If \( \gcd(a,b)=4 \) and \( ab=96 \), what is \( \operatorname{lcm}(a,b) \)?
Choose one option.
Show answer
- D. \( 24 \)
Explanation
By the relation \( \operatorname{lcm}(a,b)\cdot\gcd(a,b)=ab \), we get \( \operatorname{lcm}(a,b)=96/4=24 \). The option with 384 comes from multiplying instead of dividing.
Review the concept: Least common multiple
The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both, denoted \( \operatorname{lcm}(a,b) \).
\[\operatorname{lcm}(a,b)=\dfrac{|ab|}{\gcd(a,b)}\]
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