Lcm and Gcm

Question

When to know to find a lcm and a gcm doing a unlike fractions and when to know to reduce a fraction after you get your answer

Answer 1

When you are adding, subtracting or comparing two fractions with unlike denominators you can find the Least Common Multiple of the denominators (often referred to as finding the least common denominator) to aid in rewriting the fractions with matching denominators. You can use the listing method (listing the multiples of each denominator and finding the smallest multiples on both lists) but if you are familiar with prime factorizations this method is preferable, because the process carries over to algebraic fractions as well.

Any time you need to simplify a fraction (or check to make sure it is simplified) you can find the Greatest Common Factor of the numerator and denominator. If the GCF is 1 the fraction is simplified, if not you divide the numerator and denominator by the GCF to simplify it. Again you can use the listing method and list all the factors of both numbers, in this case you want the largest matching numbers. Preferably if you know how, you use the prime factorization method as that carries over to algebraic fractions again.

 

Answer 2

Jeffrey

The LCM: You List the multiples of the two numbers and the smallest multiples of the numbers is the LCM. It is writing the the multiplication table for numbers and the smallest number that appears in both numbers is the LCM. In looking at these two numbers the LCM is 24. It is the smallest number that is in both numbers.

12: 12, 24, 36, 48

8:  8, 16, 24, 32

The GCM is normally used as the GCF which is the greatest common factor. This is used when two numbers are being compared. You are trying to find the largest factor that will go into each of them equally with no remainder and can not be reduced again.  For example; what is the GCF of  12 and 8. First list the factors of the two numbers. You can make a factor tree.The factors of 12: are 1,2,3,& 4; the factors of 8: are 1,2, & 4. The GCF of these two numbers is 4. it is in both factors of numbers and is the largest. You can find the LCM using the information from the GCF as well. 12 x 8 the two numbers = 96 / 4 which is the GCF =4 and it will give you the LCM of the two numbers. 96/4= 24

I hope this helps.