Exercise · ZW-LEAST-COMMON-MULTIPLE-010 · ★★☆ Intermediate
If \( \operatorname{lcm}(a,b)=180 \) and \( \gcd(a,b)=3 \), with \( a=45 \), what is \( b \)?
Choose one option.
Show answer
- A. \( 12 \)
Explanation
Since \( ab=\operatorname{lcm}(a,b)\cdot\gcd(a,b)=540 \), we get \( b=540/45=12 \). The option with 540 is the product lcm times gcd without solving for b.
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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