How do you find LCM and GCF of numbers?
For finding Least Common Multiple(LCM) and Greatest Common Factor(GCF) of two numbers: 1) We first have to find out the factors of given numbers in terms of prime numbers Example :- 12 = 2*2*3 56 = 2*2*2*7 2) For 2 numbers : We have to separate out common factors and uncommon factors Example :- In 12 and 56 12 = 2*2*3 ; 56 = 2*2*2*7 Common factors = 2,2 Uncommon factors = 3,2,7 Here, GCF = Product of Common factors i.e. 2*2 = 4 and LCM = (Product of Common factors)*(Product of Uncommon factors) i.e. (2*2)*(3*2*7) = 168 For 3 numbers : We have to separate out common factors, common factors in 2 numbers and uncommon factors Example :- In 12, 48 and 56 12 = 2*2*3 ; 48 = 2*2*2*2*3 ; 56 = 2*2*2*7 Common factors = 2,2 Common factors in 2 numbers = 3(in 12 and 48), 2(in 48 and 56) Uncommon factors = 2, 7 Here, GCF = Product of Common factors i.e.2*2 = 4 and LCM = (Product of Common factors)*(Product of Uncommon factors)* (Product of common factors in 2 numbers) i.e.(2*2)*(3*2)*(2*7) = 336 For more numbers.
The LCM, or "least common multiple," is the smallest multiple that two numbers have in common. For example, the multiples of 3 are 3, 6, 9, 12, etc. The smallest multiple that 3 has in common with 2 is 6. Thus the LCM of 3 and 2 is 6.
Usually you can figure this out just by looking at the first few multiples of both numbers. If that doesn't work, multiply them together (2*3 = 6)... multiplying them together doesn't always give you the LCM, but it always gives you some multiple, and often it is indeed the LCM. A factor is like the opposite of a multiple- for example, the factors of 12 are 1, 12, 2, 6, 3, and 4.
(1*12 = 12, 2*6 = 12, 3 *4 = 12). The GCF, greatest common factor, is the biggest factor that two numbers have in common. For example, the factors of 10 are 1, 10, 2, and 5, so the GCF of 10 and 12 is 2.
There's an easy way to find the GCF scientifically. Do a "prime factorization" of both numbers. This means that you make a little tree diagram- take two factors of the number- each one is a branch.
If one of the new numbers has factors, then make two more branches for it. Eventually all the numbers you have left will be "primes"- there will be no factors except for 1 and the number itself. Multiply all the prime factors together, and you get your number.
To get the GCF, take the prime factors that your two numbers have in common, then multiply those prime factors together. Example- 12 and 24 have two 2's and one 3 in common.
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