LCM(Least Common Multiple)
LCM is defined as the smallest common multiple of two or more numbers. The Least number is exactly divisible by each of the given numbers. By making multiples of each of the numbers one time a number, two times a number, and so on. We can find a multiple that is the same for all numbers. lcm will be used in real-time applications.
It is used in music studios to calculate lcm to know how many beats per minute they need.
LCM by Division Method
To find the lcm of numbers apiece disconnection procedure, we separate a system for accomplishing something accompanying prime numbers and stop the disconnection process when we take only 1 in the last row. Observe the steps to find the lcm:
- Step 1: Divide information for one minimal prime number aforementioned that the prime number bears not completely separate 1 likely number.
- Step 2: Write the quotients right beneath the procedure in the next row.
- Step 3: Now, for the next breach step deal with duplicate quotients as the new profits.
- Step 4: Think of a prime number repeated that particularly divides not completely 1 of the profits.
- Step 5: Repeat the steps till we take 1 in the last row.
- Step 6: Multiply all the prime numbers person or group favoring the change-help side of a group of judges. That will be necessary lcm.
LCM by Prime Factorization
To calculate the LCM of some likely numbers utilizing the prime factorization system, we trail the steps likely beneath.
- Step 1: List the prime determinants of the likely numbers and note the prevailing prime determinants.
- Step 2: The lcm of the likely numbers = crop of the coarse prime determinants and the exceptional prime determinants of the program.
A factor is defined as a number that divides another number with no remainder. It is expressed as a product of whole numbers. A Factor of a number includes itself and 1. These are the trivial factors. So we don’t include factorization and it includes 1 or number itself. Prime numbers have two factors themselves, and 1 is called prime factors.
A prime factor is a factor of a number itself. If we take an example, 12 has six factors 1, 2, 3, 4, 6, and 12 but only two of them are prime, (i.e.2 and 3) so it has only two prime factors.
Types of Factors
- Even Factors: The number that is divisible by 2 is called the even factor.
- Odd Factors: The number that is not divisible by 2 is called the odd factor.
- Perfect Square Factors: A number is said to be a perfect square if its prime factors must have even powers.
Examples for Factors
Example 1: Find the factors for 12.
Solution: Here, 3 and 6 are factors for 12. Because 12 is divided by both 3 and 6. Other factors of 12 are 1,2, and 4.
Example 2: Find the Prime Factors of 15?
Solution: Any of the prime numbers that can be multiplied to give the original number is called the prime factor. Here, 3*5=15 so 3 and 5 are prime factors of 15.
Example 3: Find the Even Factors of 540?
Solution: We are multiplying the number of odd factors by a power of 2 to find the number of even factors. Here, for 540 we are having (3+1)(1+1)(2)=16 even factors.
Example 4: Find the Odd Factors of 12?
Solution: We need to exclude the even prime factor 2 to find the odd factor. Here, 12 is having 1,2,3,4,6,12 as odd factors.
Students can practice questions to better understand the concept of LCM and factors by attending online Math classes at Cuemath.