Exercise · ZW-LEAST-COMMON-MULTIPLE-006 · ★★☆ Intermediate
Compute \( \operatorname{lcm}(12, 20) \) using prime factorization.
Choose one option.
Show answer
- A. \( 60 \)
Explanation
Since \( 12=2^2\cdot 3 \) and \( 20=2^2\cdot 5 \), we take \( 2^2\cdot 3\cdot 5=60 \). The option with 240 multiplies both numbers without 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 \( \operatorname{lcm}(a,b) \).
\[\operatorname{lcm}(a,b)=\dfrac{|ab|}{\gcd(a,b)}\]
More practice problems: least common multiple
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- ZW-LEAST-COMMON-MULTIPLE-005 Two buses leave a stop, one every 8 minutes and the other every 14 . After how many minutes do they…
- ZW-LEAST-COMMON-MULTIPLE-007 If gcd(a,b)=4 and ab=96 , what is lcm(a,b) ?
- ZW-LEAST-COMMON-MULTIPLE-008 What is the least common multiple of 8 , 9 and 10 ?
- ZW-LEAST-COMMON-MULTIPLE-009 Let a=2^3· 3^2 and b=2· 3· 5^2 . What is lcm(a,b) ?
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