Least common multiple
The least common multiple of two numbers is the smallest positive integer that is the multiple of both numbers in question. It is also called the lowest common multiple or the smallest common multiple.
Example: It is necessary to find the least common multiple of numbers 6 and 8. The multiples of the number 6 are 6, 12, 18, 24, 30, 36, 42, 48…, while the multiples of the number 8 are 8, 16, 24, 32, 40, 48, 56… The common multiples of the two numbers are 24 and 48. The lesser of the two is 24 and therefore 24 is the least common multiple of the numbers 6 and 8. There is also a method to calculate the LCM using prime numbers, similar to the method used to find the greatest common factor, but it is less effective for finding the LCM. The usefulness of the LCM is the most apparent while adding, subtracting or comparing fractions. Finding the LCM of the denominators you are currently calculating with (also called the lowest common denominator) enables you to express the fractions in question as a fraction of the LCM. In other words, all of the fractions can be expressed as fractions of the same denominator, which is the lowest common denominator of all the denominators.
The least common multiple can also be calculated for rational numbers while using the same principle.
Example: We need to calculate the least common multiple of the rational numbers 2/5 and 4/7. The multiples of the number 2/5 are 4/5, 6/5, 8/5, 10/5, 12/5, 14/5, 16/5, 18/5, 20/5… and the multiples of the number 4/7 are 4/7, 8/7, 12/7, 16/7, 20/7, 24/7, 28/7…, their least common multiple is 4 (20/5=28/7=4).
Knowledge of the least common multiple of two or more numbers is very useful while adding, subtracting or comparing fractions that have different denominators.
Least common multiple exams for teachers
Exam Name  File Size  Downloads  Upload date 
Integers


Least common multiple of integers – very easy  551.6 kB  2906  October 13, 2012 
Least common multiple of integers – easy  558 kB  2719  October 13, 2012 
Least common multiple of integers – medium  548.9 kB  2946  October 14, 2012 
Least common multiple of integers – hard  550.4 kB  1562  October 13, 2012 
Least common multiple of integers – very hard  553.8 kB  1472  October 13, 2012 
Monomials


Least common multiple of monomials – very easy  573.9 kB  1427  October 13, 2012 
Least common multiple of monomials – easy  582.5 kB  1081  October 13, 2012 
Least common multiple of monomials – medium  574.5 kB  1280  October 13, 2012 
Least common multiple of monomials – hard  552.9 kB  992  October 13, 2012 
Least common multiple of monomials – very hard  550.5 kB  1017  October 13, 2012 
Least common multiple worksheets for students
Worksheet Name  File Size  Downloads  Upload date 
Least common multiple of integers  154.6 kB  2527  October 14, 2012 
Least common multiple of monomials  277 kB  1451  October 14, 2012 