Exercise · ZW-LEAST-COMMON-MULTIPLE-005 · ★★☆ Intermediate
Two buses leave a stop, one every \( 8 \) minutes and the other every \( 14 \). After how many minutes do they depart together again?
Choose one option.
Show answer
- B. \( 56 \)
Explanation
Since \( 8=2^3 \) and \( 14=2\cdot 7 \), the first meeting occurs after \( 2^3\cdot 7=56 \) minutes. The option with 2 is the greatest common divisor, not the least 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-003 When adding (1)/(4) and (1)/(10) , what is the smallest possible common denominator?
- 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-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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