The least common multiple is the smallest positive integer that is divisible by both given numbers.
The Least Common Multiple (LCM) of a group of numbers is the smallest number that is a multiple of all the numbers. For instance, the LCM of 16 and 20 is 80; 80 is the smallest number that is both a multiple of 16 and a multiple of 20. You can find the LCM of two or more numbers through various methods.
This is an ideal method for larger numbers.This method is factoring both numbers down to the prime numbers that are multiplied to create that number as a product.
For Example :- Let's say you're looking for the least common multiple of 20 and 42. Here's how you would factor them 20 = 2 x 2 x 5 and 42 = 2 x 3 x 7
If the number just occurs in one number, then it has one occurrence. Here is a list of the most occurrences of each prime number from the previous example 2 → 2 times 3 → 1 time 5 → 1 time 7 → 1 time
Since 2 occurs twice, you'll have to multiply it twice. Here's what you should do to find the LCM: 2 x 2 x 3 x 5 x 7 = 420.
Write the numbers at the top of the Common Factors Grid (as shown in the example). Leave a small space to the left of the numbers and as much space as you can below the numbers. Let's say we're working with the numbers 18, 12, and 30. Just write each number down in its own row at the top of the grid.
Write the lowest common prime factor of the numbers in the space to the left. Just look out for the smallest prime factor (such as 2, 3, or 5) that you can pull out of all the numbers. They're all even, so you can pull out 2.
Divide each of the original numbers by the common prime factor. Write the quotient below each number. Here's how to do it:
18/2 = 9, so write 9 below 18.
12/2 = 6, so write 6 below 12.
30/2 = 15, so write 15 below 30.
Repeat the process of pulling out and dividing by the lowest prime factor until no more common factors exist. Just repeat the process from the previous steps using the numbers 9, 6, and 15 this time.
Pull out a 3 from these numbers. 3 is the lowest prime factor, or the smallest prime number that is evenly divisible by both numbers. Find the Least Common Multiple of Two Numbers
Divide all three numbers by 3 and write the result below those numbers. Find the Least Common Multiple of Two Numbers
9/3 = 3, so write a 3 below the 9; 6/3 = 2, so write a 2 below the 6; 15/3 = 5 so write a 5 below the 15.
If two of the numbers still share a prime common factor, then continue the process until no pair of bottom numbers have a common factor. In this particular example, you're done.
For example, if the bottom three numbers are 2, 39, and 122, divide 2 and 122 by 2 leaving the new bottom row as 1, 39, and 61.
Multiply all the numbers of the first column containing the common prime factors with the numbers at the bottoms of all the other columns. This is the LCM. In this example, the product of the common factor column is 6 (2 x 3). Multiply 6 by the numbers at the bottoms of the other columns: 6 x 3 x 2 x 5 = 180.
The LCM of 18, 12, and 30 is 180.
The first container will fill the tanker by 11 times and the second will by 5 times.