Math Problem Statement

Find the least number which is exactly divisible by each one of the numbers 12, 16 and 24.

Solution

To find the least number that is exactly divisible by 12, 16, and 24, we need to determine the Least Common Multiple (LCM) of these numbers.

Steps to find the LCM:

  1. Prime factorization of each number:

    • 12=22×312 = 2^2 \times 3
    • 16=2416 = 2^4
    • 24=23×324 = 2^3 \times 3
  2. Identify the highest powers of all prime factors:

    • For 22: The highest power is 242^4 (from 16).
    • For 33: The highest power is 313^1 (from 12 and 24).
  3. Multiply these highest powers together to find the LCM: LCM=24×31=16×3=48\text{LCM} = 2^4 \times 3^1 = 16 \times 3 = 48

So, the least number that is exactly divisible by 12, 16, and 24 is 48.

Would you like further details or have any other questions?

Here are five related questions:

  1. What is the LCM of 8, 14, and 21?
  2. How do you find the LCM of two numbers using the prime factorization method?
  3. What is the greatest common divisor (GCD) of 12, 16, and 24?
  4. Can a number be a multiple of 12, 16, and 24 but not the LCM?
  5. What is the smallest number divisible by 15, 20, and 30?

Tip: The LCM of a set of numbers is the smallest number that all of the numbers divide into without leaving a remainder.

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Math Problem Analysis

Mathematical Concepts

Number Theory
Prime Factorization
Least Common Multiple (LCM)

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8