Lowest Common Multiple

The lowest common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given numbers. The concept is fundamental in arithmetic and number theory, often used in problems involving fractions, ratios, and periodicity.

The lowest common multiple (LCM) is the smallest positive integer that is evenly divisible by two or more given numbers. It represents the “least common” value that is a multiple of each number.

Example:
The LCM of 4 and 6 is 12, as 12 is the smallest number divisible by both 4 and 6.

The prime factorization method involves expressing each number as a product of its prime factors and then using these factors to compute the lowest common multiple (LCM)

Example: Find the LCM of 12 and 18.

1. Break each number into its prime factors.



2. Combine all the prime factors found in the numbers. In this case, the primes are 2 and 3.

3. For each prime, take the largest exponent (power) that appears in the factorization:
For , the highest power is
For , the highest power is

4. Multiply the selected prime factors and their powers:

The repeated division method is another way to find the lowest common multiple (LCM) of two or more numbers. This method uses successive divisions by prime numbers, which is especially helpful for larger numbers.

For any two prime numbers, their LCM is always the product of the two numbers.

Example: Find the LCM of 3 and 5

• Real Numbers
• Whole Numbers
• Integers
• Rational Numbers
• Irrational Numbers

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