Free worksheets for the greatest common factor (GFC) and least common multiple (LCM)
Students show what they know about GCF and LCM. Plan your minute lesson in Math or Number Sense and Operations with helpful tips from Ursula Lovings. Greatest Common Factor of 3 Numbers Online Quiz - A tutorial to learn maths in simple and easy steps along with word problems, worksheets, quizes and their. Learn about and revise different types of numbers such as primes, factors, multiples and powers with GCSE Using prime factors to find the HCF and LCM.
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Math : Finding the LCM Quiz
It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. This corresponds to the least exponent of the factor 2. So to get the GCF of two numbers, we only need to take the common prime factors from the prime factorizations and compare their exponents.
In each case, we take the exponential expression that has the least exponent and multiply those together. We reconsider the previous example to illustrate the use of the exponents. The least exponent for 2 is 3 23for 3 is 2 32and for 11 is 1 A machine contains two gears.
One gear has 12 teeth and the other has 20 teeth.
Find the LCM and the GCF of Integers - Examples and Questions with Answers (Grade 5)
The gears are aligned by a mark drawn from the center of the first gear to the center of the second gear. What is the smallest number of revolutions of the first gear necessary to realign the mark? We begin by listing, for each gear, the number of teeth that would pass the starting mark after the first revolution, second revolution, third revolution, …. The first gear will be aligned with the second gear after five revolutions.
Also, note the second gear will have made three revolutions. This question was answered using the least common multiple.
Notice that the mark on the first gear returns to its original position after each full revolution. This will happen when it has gone through 12 teeth, 24 teeth, 36 teeth, etc.
The mark on the second gear returns to its original position after it has made any number of full revolutions. This will happen when it has gone through 20 teeth, 40 teeth, 60 teeth, 80 teeth, etc.
Greatest Common Factor and Least Common Multiple
Notice that 12, 24, 36, … are multiples of 12 and 20, 40, 60, … are multiples of The mark will be realigned only when a value that is both a multiple 12 and of 20 is reached. The mark will be realigned for the first time when the first such multiple is reached.
Therefore, we are looking for the Least Common Multiple of 12 and The least common multiple LCM of two natural numbers n and m is the smallest valued number h so that h is a multiple of both n and m. Relating this definition to the problem we solved on the previous page, we see that the two numbers n and m are the numbers 12 and This says "the least common multiple of 12 and 20 is It has the least value if the multiples shared by both n and m.
The number h is the Least Common Multiple of 12 and One method for finding the least common multiple is to choose the value that is the minimum value in the intersection of the sets of multiples.
- Hcf And Lcm Quiz
- GCF and LCM Quiz
- Multiples, factors, powers and roots
Find the LCM 12, We find the set of their natural number multiples and then find the least value in the intersection of the two sets. Notice that the intermediate step in the problem gives all the common multiples. Since we have found the least common multiple, 60, for the gear problem, we can now answer the question to the gear problem.