LCM of 4 and 7

LCM is the smallest positive integer which is a multiple of both 4 and 7. LCM of 4,7 = 28
 

Here different ways are explained to find LCM as; Listing method, prime factorization method and division method
 

Step 1: Record the multiples of each number;

4  = 4,8,12,16,20,24,28,…

7 = 7,14,21,28…

Step 2: Pick among the smallest multiple of 4 and 7 LCM

LCM(4,7) = 28

We write down the prime factors of each number and multiply the highest power of those common prime factors to get LCM.

Step 1: List the numbers in prime factor form:

Prime factorization of 4 = 2×2

Prime factorization of 7 = 7

Step 2: Multiply the maximum powers of each prime.

— 2,2,7

LCM(4,7) = 28

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

Step 1: Write down the numbers in a row;

Step 2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers that have not been divisible previously.
  
Step 3: The LCM of the numbers is the product of the prime numbers in the first column, i.e, 

2×2×7= 28

LCM (4,7) = 28

• Multiple: A number and any integer multiplied. 

• Prime Factor: A natural number (other than 1) that has factors that are one and itself.

• Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 

• Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 

• Relatively Prime Numbers:     Numbers that have no common factors other than 1.

• Fraction: A representation of a part of a whole.