Exercise · ZW-LEAST-COMMON-MULTIPLE-009 · ★★★ Advanced
Let \( a=2^3\cdot 3^2 \) and \( b=2\cdot 3\cdot 5^2 \). What is \( \operatorname{lcm}(a,b) \)?
Choose one option.
Show answer
- B. \( 1800 \)
Explanation
Take the largest exponent of each prime: \( 2^3\cdot 3^2\cdot 5^2=8\cdot 9\cdot 25=1800 \). The option with 3600 doubles the result by using an extra factor of 2.
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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