Q: How can you use prime factorization to find the LCM of 15 and 21?

Write your answer...

Submit

Still have questions?

Continue Learning about Basic Math

Prime factorization helps to find the greatest common factor and the least common multiple which, in turn, help in the adding, subtracting and reducing of fractions.

The LCM of 25 and 30 is: 150The prime factorization of 25 = 5x5The prime factorization of 30 = 2x3x5GCF = 5But, what is the use of calculating GCF here?Answer: If we divide the product of 25 and 30 by GCF then the result is LCM.Product of 25 & 30 = 25x30 = 750So, LCM = 750/5 =150Least Common Multiple (LCM) for 25 30 is 150

what is the fatorization of 54

Lets investigate. To find an LCM you do a prime factorization and choose the factors, which are not in common raised to an appropriate power to show how many times it occurs in one of the 2 numbers AND use all factors that they do not have in common also to an approp. power. Ex 1 LCM of 49 and 25 prime factorization yields 5x5 and 7x7 SO LCM will be (5x5)x(7x7) because they have no common factors which equals 352 Ex 2 LCM of 100 and 36 prime factorization yields 5x5x2x2 and 3x3x2x2 They have common factors of 2x2 so use these but dont repeat them So LCM = (5x5)x(3x3)x(2x2) = (5x3x2)x(5x3x2) = 302 So every square (A) when factored becomes either (a x a) or (b x b x c x c) etc. Lets find the LCM of A and N where A and N are squares, but not equal. Prime factorization A = ( a x a x b x b) and N = ( n x n x p x p x a x a) LCM will equal (b x b) x ( n x n x p x p) x (a x a) <-- common factors = (a x b x n x p) x (a x b x n x p) = (a x b x n x p)2 which is a square. The rules for forming a LCM force you to make a square because each original number has a prime factorization that has 2 factors, and you must use both or you will not form a LCM.

Use a factor tree. 400 200,2 100,2,2 50,2,2,2 25,2,2,2,2 5,5,2,2,2,2

Related questions

True.

You need at least two numbers to find an LCM no matter what you use.

speed you can just use your brain to find the LCM faster, sometimes.

To answer GCF and LCM questions.

To find the GCF and the LCM you have to first at least try to use prime factorization. So use factor trees. Or for the LCM find th least common multiples of the number.

It doesn't matter which method you use. You still need at least two numbers to find an LCM. There is no LCM of 20.

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.

In finding the LCM or HCF of two or more numbers

The prime factorization of 560 is: 2, 5, and 7

you use prime factorization

3 x 5 = 153 x 7 = 213 x 5 x 7 = 105, the LCM

a and b have no common prime factors. Their LCM is their product.