The LCM or least common multiple often needs to be calculated for two or more numbers. There are several established methods used to calculate the LCM, but the method in this lesson plan can be expanded to find the LCM of three or more numbers, and is easier to understand for basic level math studies.
What Is The Least Common Multiple?
The least common multiple of two numbers is the smallest positive whole number that can be divided by each of the two numbers without leaving a remainder. When dealing with fractions, the least common multiple is usually the lowest common denominator that may be used. One of the most common reasons for calculating the LCM is to enable the addition or subtraction of fractions.
Prime Factors and Factorization
The first step to be taken when finding the LCM of a set of numbers is to factorise each of the numbers into it's prime factors. This process is described in the article "Finding The Prime Factors Of A Number".
Calculating The Least Common Multiple
Figure 1 shows the prime factors of 14 and 24 visually. The least common multiple of 24 and 14 may be described as the number that contains all of the factors of each number. In other words, any number that divides into 24 or 14 should divide the LCM. The LCM could be thought of as the lowest number into which all of the factors of 24 and 14 could be "fitted". With that in mind, the right hand side rectangle in figure 1 shows that the LCM needs to contain 2 x 2 x 2, 3, and 7.
So the LCM of 24 and 14 is 2 x 2 x 2 x 3 x 7 = 168.
Least Common Multiple Lesson Plan Summary
Least common multiple is useful when teaching and manipulating fractions. The process to find the LCM for two or more numbers at a time involves knowing the first few prime numbers, then finding the prime factors for each number, deducing the prime factors of the LCM, and multiplying these together to find the LCM itself. The LCM Ready Reckoner (Figure 2) shows the least common multiples for the numbers from 1 to 24.
The LCM may also be calculated easily if the Greatest Common Divisor is known.
The Excel function "LCM" may be used, but it contains a slight bug:
=LCM(24,14) will give the correct answer 168, but
=LCM(24, 14.1) will also produce the answer 168. This may or may not be a problem for the user.
Least Common Multiple and Prime Factorization References
Most of the information here is widely known and available, although the DVD "Math Mystery Theater: Fractions: Multiple Adventures of Math Man: Least Common Multiples DVD (Interest Levels 3-Adult)" and the CD " Math Skill Builders: Set 3: Finding Multiples " are useful resources.
Martin Bell - Martin holds a B.Sc. degree in chemical engineering, and an M.Sc. degree in electronics and computing. He has spent more than 25 years ...
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