6 — Multiples and Common Multiples

Multiples and Common Multiples

Solution & Explanation · ID: 2066E53C

Question

Find the LCM of 9 and 15.

Hint

List multiples of each number until you find the smallest one they share.

Concept

The Least Common Multiple (LCM) is the smallest positive number that is a multiple of two or more given numbers. We can find it by listing multiples or using prime factorization.

Show Answer

45

Show Solution
1

List the multiples of 9: 9, 18, 27, 36, 45, 54, 63...

2

List the multiples of 15: 15, 30, 45, 60, 75...

3

Find the first number that appears in both lists

4

The smallest common multiple is 45, so LCM(9, 15) = 45

Two horizontal lists. Top list labeled 'Multiples of 9' shows: 9, 18, 27, 36, 45, 54, 63. Bottom list labeled 'Multiples of 15' shows: 15, 30, 45, 60, 75. The number 45 is highlighted with a star in both lists and has an arrow pointing to it with text 'LCM = 45'.