LCM of 3, 5 and 10

The LCM of 3, 5 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators. 
 

There are various methods to find the LCM. The methods to find the LCM are:

• Listing method

• Prime factorization method  

• Division method 
   

In the listing method, we write a multiple of the numbers first and then find the smallest common multiple.

Step 1: Identify the multiples of 3, 5 and 10

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….

Multiples of 5:   5, 10, 15, 20, 25, 30, 35, 40, 45, 50….

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90….

Step 2: Ascertain the smallest multiple from the listed multiples of 3, 5 and 10

The LCM of 3, 5 and 10 is 30
 

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Step 1: Find the prime factors of 3, 5 and 10

Prime factorization of 3: 3¹

Prime factorization of 5: 5¹

Prime factorization of 10: 2¹ × 5¹

Step 2: Multiply the highest power of each factor ascertained to get the LCM 

LCM of 3, 5 and 10 = 2¹  × 3¹ × 5¹  = 30

This method involves simultaneously dividing the numbers by their prime factors until they become 1 and multiplying the divisors to get the LCM. 

Step 1: Write the numbers in a row, like 3, 5, 10.

Step 2: Start dividing the numbers with prime factors by 2 

From the numbers 3, 5 and 10, only 10 is divisible by 2 (10 ÷
2) which gives 5 as the quotient.

Now the numbers in the row will be 3, 5, 5

Step 3: Move on to the next prime number, 3

From the list 3, 5 and 5, only 3 is divisible by 3 (3 ÷ 3) which gives 1 as the quotient.

Now the numbers in the row will look like 1, 5, 5.

Step 4: Move on to the next prime number 5.

 From the list 1, 5 and 5, only 5 is divisible by 5 (5 ÷ 5) which gives 1 as the quotient.

Now the numbers in the row will look like 1, 1, 1.

Step 5: To find the LCM, multiply all the divisors used 

The divisors used are 2, 3 and 5. The product of 2, 3 and 5 is 30 (2×3×5 = 30)

• 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. 

• LCM: The least common multiple is the smallest number divisible by two or more numbers.