Exercise · ZW-LEAST-COMMON-MULTIPLE-003 · ★★☆ Intermediate
When adding \( \frac{1}{4} \) and \( \frac{1}{10} \), what is the smallest possible common denominator?
Choose one option.
Show answer
- D. \( 20 \)
Explanation
The denominators \( 4=2^2 \) and \( 10=2\cdot 5 \) give the least common multiple \( 2^2\cdot 5=20 \). The option with 14 adds the denominators instead of finding a common multiple.
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
- ZW-LEAST-COMMON-MULTIPLE-001 What is the least common multiple of 4 and 6 ?
- ZW-LEAST-COMMON-MULTIPLE-002 What is the least common multiple of 5 and 7 ?
- ZW-LEAST-COMMON-MULTIPLE-004 If gcd(a,b)=1 , with a=14 and b=15 , what is lcm(a,b) ?
- 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-006 Compute lcm(12, 20) using prime factorization.
- 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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