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What do you use prime factorization for?
To answer GCF and LCM questions.
What is the LCM of 540 and 315?
Steps to find out LCM of two numbers(a & b):1- Find HCF of a & b.2- Multiply a and b.3- Divide the result of step 2 by HCF. The result is LCM.1- In order to find out HCF of 540 and 315 we shall use the method of prime factorization.Prime factorization of 540 = 2x2x3x3x3x5Prime factorization of 315 = 3x3x5x7HCF(540, 315) = 3x3x5 = 45.2- Product of 540 and 315.540 x 315 = 170100.3- LCM(540, 315) = 170100/45 = 3780.
How can you use the prime factorization of two numbers to find the LCM?
You can use the numbers in common in the prime factorization to find the LCM (least common multiple of two numbers). Multiply all the prime factors together, but if the two numbers have a prime factor in common, only use that number once. Here are a few examples: Find the LCM of 40 and 35: The prime factorization of 40 is 2*2*2*5. The prime factorization of 35 is 5*7. The prime factorization both have a 5 in common, so you only need one five. The LCM then is 2*2*2*7*5 = 280. Find the LCM of 24 and 20: 24 = 2*2*2*3. 20 = 2*2*5. The prime factorization have two twos in common, so you only need one two from each pair. You will still need another 2 since the third 2 in the prime factorization of 24 does not have a pair in the factorization of 20. The LCM then is 2*2*2*3*5 = 120. Find the LCM of 15 and 4: 15 = 3*5 4 = 2*2 There are no matching pairs between the prime factorization, so find the LCM by multiplying all the numbers together: 2*2*3*5=60 Find the LCM of 60 and 100: 140 = 2*2*3*5 100 = 2*2*5*5 There are two pairs of 2s and a pair of 5. You can think of it like this: 140 = (2*2*5)*3 100 = (2*2*5)*5 The numbers in parentheses are pairs so you only need one of them. In this case, the LCM is (2*2*5)*3*5 = 300.
Where do you use prime factorization in real life?
In finding the LCM or HCF of two or more numbers
What is the least common multiple of 9 12 and15?
The LCM of 9,12, and 15 is 180.Let's use prime factorization to see why?9=32,12=22 x315=3x5.To find the LCM take 32 , 22 , and 5.9x4x5=180 which is the answer. Note we took the largest exponent of each of the factors and their product is the LCM.
