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Least Common Multiple (LCM) Calculator

Find the least common multiple step by step

The calculator will find the least (smallest) common multiple of the given positive numbers, with steps shown, using either the factoring method or the prime factorization method.

Enter numbers (comma-separated) or

Your input:

Positive numbers, separated by commas, for example, `20, 10, 35`.

Choose a method:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Solution

Your input: find theLCM of $$$8, 72, 24$$$ using factoring.

The LCM of numbers is the smallest number that is divisible by all given numbers.

Find some multiples of each number.

  • Multiples of $$$\color{Green}{8}$$$: $$$8, 16, 24, 32, 40, 48, 56, 64, \color{Red}{72}, 80, 88, 96, 104$$$
  • Multiples of $$$\color{Green}{72}$$$: $$$\color{Red}{72}, 144, 216, 288, 360$$$
  • Multiples of $$$\color{Green}{24}$$$: $$$24, 48, \color{Red}{72}, 96, 120, 144, 168, 192$$$

The smallest common (all numbers share it) multiple is highlighted.

Thus, $$$LCM\left(8, 72, 24\right)=72$$$.

Answer: $$$LCM\left(8, 72, 24\right)=72$$$.

Related Note: Least Common Multiple (LCM)