What is the least common denominator of 1/5 and 1/9?

What is the least common denominator of 1/5 and 1/9?

• A. 45
• B. 5
• C. 15
• D. 9

Answer: (A)

Finding the least common denominator means locating the smallest number that can serve as a common bottom for both fractions. You need a number that both 5 and 9 divide into evenly. Because 5 and 9 have no common factors other than 1, their least common multiple is 5 × 9 = 45. So the least common denominator is 45. You can rewrite each fraction with denominator 45: 1/5 = 9/45 and 1/9 = 5/45, which shows both share the same denominator. Trying smaller denominators won’t work since 5 doesn’t accommodate a multiple of 9 and 9 doesn’t accommodate a multiple of 5; 15 is a multiple of 5 but not of 9, and 9 is a multiple of 9 but not of 5. Therefore 45 is the smallest common denominator.

Finding the least common denominator means locating the smallest number that can serve as a common bottom for both fractions. You need a number that both 5 and 9 divide into evenly. Because 5 and 9 have no common factors other than 1, their least common multiple is 5 × 9 = 45. So the least common denominator is 45. You can rewrite each fraction with denominator 45: 1/5 = 9/45 and 1/9 = 5/45, which shows both share the same denominator. Trying smaller denominators won’t work since 5 doesn’t accommodate a multiple of 9 and 9 doesn’t accommodate a multiple of 5; 15 is a multiple of 5 but not of 9, and 9 is a multiple of 9 but not of 5. Therefore 45 is the smallest common denominator.