LCM Calculator - From Multiple Integers

Calculator

• enter your numbers into the input field, separated by spaces or commas (e.g., 4, 6, 8 or 4 6 8)

Result

• the Least Common Multiple calculated from the numbers you entered

Least Common Multiple (LCM)
Definition: The LCM of two or more integers is the smallest positive integer that is divisible by each of the integers.
Purpose: It is used to find common multiples, synchronize cycles, and solve problems involving multiples.

Example Calculation:

For numbers 48 and 18, the LCM is calculated as follows:

Find the prime factors:
48 = 24 * 3
18 = 2 * 32
Identify the highest power of each prime factor:
24
32
Multiply these together: 24 * 32= 16 * 9 = 144.

Therefore, the LCM of 48 and 18 is 144.

Alternatively, make a list of multiples for each number:
Multiples of 48: 48, 96, 144, 192, 240, etc.
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, etc.
Common Multiples: 144, 288,...

Least: 144

LCM is helpful in various mathematical problems, including algebra and number theory, where finding common multiples is required.
Useful Example
If you have two tasks, one that repeats every four days and another every six days, you can use the LCM to find out when both will happen on the same day. The LCM of 4 and 6 is 12, so both tasks will coincide every 12 days.
Understanding the LCM and its applications can simplify solving many problems involving multiple and periodic events.

Negative Integers

Find the LCM of 3, 4, and 6:

LCM(3, 4, 6) = 12

Explanation: 12 is the smallest positive integer divisible by 3, 4, and 6 without leaving a remainder. It is positive because it represents a common multiple of the given numbers.

Find the LCM of -2, 5, and -10:

LCM(-2, 5, -10) = 10

Explanation: The LCM is still a positive integer, even when dealing with negative numbers. This is because the sign of the numbers does not affect their divisibility. The LCM is the same as the LCM in terms of their absolute values, which are positive.

The LCM is always a positive integer because it represents the smallest positive multiple shared by all the given numbers, regardless of their signs.