0
Still curious? Ask our experts.
Chat with our AI personalities
Maxine
Professor
SteveAdd your answer:
Earn +20 pts
How do you work out the lcm when there are indices?
It is the same as finding the LCM of two numbers that have been expressed as a product of their prime factors except that you need to use the highest index for each prime factor.
What is the least common multiple of 5 14 and 30?
The LCM of 5, 14, and 30 is 210 Answer: You calculate the prime factors for each number, write them down, then use each prime number once (or in the highest power in which it appears in any of the factors) in the result.
How do you find the least common multiple of two numbers?
LCM is the multiple of the highest power of prime factors in the numbers. Example: LCM 0f 9 and 25 is 225, which is the multiple of the highest power of prime factors in 9 and 25 (32 x 52).The LCM of two or more numbers is the product of all the prime factors to their greatest power.An example of how use this method:Prime factors of 27 are 33Prime factors of 30 are 2 x 3 x 5Prime factors of 12 are 22 x 3Prime factors of 8 are 23The LCM of 27, 30, 12, and 8 is 23 x 33 x 5= 8 x 27 x 5 = 1,080
Why is the LCM of two square numbers always another square number?
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.
How do you use the prime factorizations to find the LCM of 25 and 30?
5 x 5 = 25 2 x 3 x 5 = 30 Combine the factors, eliminating duplicates. 2 x 3 x 5 x 5 = 150, the LCM.
