Least common multiple is one of the basic mathematical concepts that is started teaching to students in primary education. This is because it sets the base to solve fractional problems in different subjects such as physics, chemistry, and statistics. Apart from that, it also has many applications in real life, which makes it important to learn.
However, many learners find it difficult to calculate the LCM of two numbers. That’s why we have created this guide to help those who are still unable to solve the least common multiple questions. In this article, we will walk you through different methods to find the LCM of two numbers. However, before that, let’s first recall what LCM is.
Least Common Multiple—Definition
According to KhanAcademy, a trusted educational platform, LCM refers to the smallest number that two numbers share. In simple words, the least common multiple of two numbers is the smallest number that both of them divide evenly. An important thing to remember in this regard is that LCM can never be negative; rather, it is always a positive integer. Since it is not a measurable quantity, it is not represented by any notation or symbol. Its short form, “LCM,” is used everywhere in mathematics and other subjects.
Methods To Calculate Least Common Multiple
Let’s look at some of the easy ways to find the lowest common multiple of two numbers:
Prime Factorization Method
It is a bit of a complex method that involves first breaking down both numbers into their prime factors. However, this technique is helpful for learning purposes as it also involves the practice of factorization. Also, it is useful for large numbers that have many prime factors. Here is the complete process to use this method to find LCM:
- Break the numbers into their prime factors.
- Writing similar factors of each number in terms of power.
- Identify the highest occurrence of each factor in both numbers.
- Then, the maximum number of times any factor appears in either number is multiplied.
Example: Find the LCM of 84 and 104.
Solution:
PF of 84 = 2 × 2 × 3 × 7 = 22 × 3 × 7
PF of 104 = 2 × 2 × 2 × 13 = 23 × 13
Here, the highest occurrence of 2 is three times, and 3, 7, and 13 are one time. So, the LCM will be as follows:
LCM = 23 × 3 × 7 × 13
LCM = 2184
Listing Multiples Technique
Another method of calculating the LCM of two numbers is by finding the multiples of each number. This technique is usually beneficial when you have to find the least common multiple of small numbers. Calculating LCM using this method requires you to follow the simple steps mentioned below:
- Start listing the multiples of both numbers one by one.
- Stop the process when you get the smallest common one.
- The multiple you stop at will be the LCM of both numbers.
Example: What will be the LCM of 9 and 10?
Solutions:
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117,…
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,…
Here, it is clear that 90 is the smallest number that is present in the multiples of both 9 and 10. It means the value of LCM is 90.
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Division Method
The division method is also used to find the LCM of two numbers, especially the large ones. It is a structured way of dividing the intended numbers to get the least common multiple in just a few steps. You may call it the combination of the above two methods with a little bit of modification, as it involves both factors and multiples. Here is the process of applying this method:
- Write the numbers side by side.
- Divide them by the smallest common prime factor.
- Continue dividing until no common factor remains.
- Multiply all divisors and the remaining numbers to get the LCM.
Example: Calculate the LCM of 44 and 32 by the division method.
Solution:
Dividing given numbers by 2 → 22, 16
Dividing above numbers by 2 → 11, 8
by 2 → 11, 4
by 2 → 11, 2
by 2 → 11, 1
by 11 → 1, 1
LCM = 2 × 2 × 2 × 2 × 2 × 11
LCM = 352
Using AN Online LCM Calculator
The easiest or quickest way to compute LCM of two numbers is using an online least common multiple calculator. Whether the numbers are small or large, you don’t need to worry. Just provide the numbers to the calculator, and your LCM will be calculated within seconds.
As you input the values, the tool utilizes any of the above-mentioned methods and applies the process automatically. Whether it is prime factorization method or division method, the calculator itself does all the relevant calculations and generates an accurate LCM.
The best thing is that such tools are easily available on any device, allowing you to instantly find LCM without wasting time in manual calculations. Also, some efficient calculators also display the steps involved in finding the LCM so that you can understand the procedure.
Wrapping Up
After going through this article, we hope that you have learned the ways to calculate the LCM of two numbers. So from now on, you can easily find the least common multiple no matter what numbers are given to you.
