Answer:
The LCM of 32, 42, and 62 is 7728.
Example:
Suppose we have a group of students with 32 pencils, 42 erasers, and 62 sharpeners. We want to divide the students into equal groups such that each student has the same number of pencils, erasers, and sharpeners. What is the smallest number of students we can have in each group?
To answer this question, we need to find the LCM of 32, 42, and 62. The LCM is 7728, so the smallest number of students we can have in each group is 7728.
Explanation:
To find the LCM of 32, 42, and 62, we can use the following steps:
Prime factorize each number:
32 = 2^5
42 = 2*3*7
62 = 2*31
Find the highest power of each prime factor that occurs in any of the numbers:
2: 5
3: 1
7: 1
31: 1
Multiply the prime factors together, raised to their highest powers:
LCM(32, 42, 62) = 2^5 * 3^1 * 7^1 * 31^1 = 7728