Skip to Main Content
HBS Home
  • About
  • Academic Programs
  • Alumni
  • Faculty & Research
  • Baker Library
  • Giving
  • Harvard Business Review
  • Initiatives
  • News
  • Recruit
  • Map / Directions
Faculty & Research
  • Faculty
  • Research
  • Featured Topics
  • Academic Units
  • …→
  • Harvard Business School→
  • Faculty & Research→
Publications
Publications
  • Article
  • Canadian Mathematical Bulletin

Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

By: Daniel M. Kane and Scott Duke Kominers
  • Format:Print
ShareBar

Abstract

For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained previously when either u_0 or n is large. When r is prime, our best bound is sharp up to a factor of n+1 for u_0 properly chosen, and is also nearly sharp as n\to\infty.

Keywords

Mathematical Methods

Citation

Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
  • Find it at Harvard
  • Purchase

About The Author

Scott Duke Kominers

Entrepreneurial Management
→More Publications

More from the Authors

    • June 2025
    • Journal of Finance

    Collusion in Brokered Markets

    By: John William Hatfield, Scott Duke Kominers and Richard Lowery
    • March 14, 2025
    • Harvard Crimson

    Harvard Students Should Ignore Calls to Boycott Israel Trek

    By: Jesse M. Fried, Paul A. Gompers, Scott Kominers and Mark C. Poznansky
    • March 2025
    • Faculty Research

    O2X: Optimizing to the X

    By: Scott Duke Kominers, Thomas Jennings and Maisie Wiltshire-Gordon
More from the Authors
  • Collusion in Brokered Markets By: John William Hatfield, Scott Duke Kominers and Richard Lowery
  • Harvard Students Should Ignore Calls to Boycott Israel Trek By: Jesse M. Fried, Paul A. Gompers, Scott Kominers and Mark C. Poznansky
  • O2X: Optimizing to the X By: Scott Duke Kominers, Thomas Jennings and Maisie Wiltshire-Gordon
ǁ
Campus Map
Harvard Business School
Soldiers Field
Boston, MA 02163
→Map & Directions
→More Contact Information
  • Make a Gift
  • Site Map
  • Jobs
  • Harvard University
  • Trademarks
  • Policies
  • Accessibility
  • Digital Accessibility
Copyright © President & Fellows of Harvard College.