The Lowest Common Multiple (LCM) of two or more given number is the lowest (or smallest or least) of their common multiples.
Example: LCM of 12 and 15.
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252…
Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240…
Common Multiples of 12 and 15 are 60, 120, 180, 240…
Lowest Common Multiples of 12 and 15 is 60. (60 is the smallest number that both the numbers are factors of this number.)
Example: Find LCM of 16, 24 and 56
Step1: Find out the prime factors of the given numbers.
Prime factor of 24 = 2 x 2 x 2 x 3 = 2^{3 }x 3
Prime factor of 56 = 2 x 2 x 2 x 7 = 2^{3 }x 7
Step2: Identify the maximum number of occurrence of each prime number. Here, 2^{4 }(2 has occurred 4 times), 3^{1} (3 has occurred 1 time) and 7^{1} (7 has occurred 1 time)
Step3: Now multiply the outcomes.
2 x 2 x 2 x 2 x 3 x 7 = 336
Step 1: Find the prime factors of the two or more numbers by dividing the numbers by least prime number till we get 1. (Choose the least prime that at least divide one of the given numbers)
Step 2: Then multiply all the prime factors to get the LCM.
Example: Find LCM of 20, 25 and 30
LCM of 20, 25 and 30 = 2 x 2 x 3 x 5 x 5 = 300