LCM of 9,12 and 18

The LCM of 9,12 and 18 is 36. How did we find this?
Let us learn!
 

The LCM of 9,12 and 18 can be found using three methods;

• listing multiples method,

• prime factorization method 

• division method.

The mentioned are explained below; 
 

In this method, we list the multiples of the numbers given until we land at the smallest multiple that is common between the numbers. 

To elaborate; 

Multiples of 9 = 9,18,27,36,…

Multiples of 12 = 12,24,36,…

Multiples of 18 = 18,36,...

From the above we can clearly see that the smallest common multiple between the numbers is 36, which is the LCM of 9,12 and 18. 

LCM (9,12,18) = 36 
 

Here, we factorize the numbers into their prime factor and multiply the highest powers to find the LCM. 

Substantiating the above; 

Step 1. Prime factorize the numbers,

9 = 3×3

12 = 2×2×3

18= 2×3×3

Step 2. Multiply the highest powers 

Step 3. Multiply the factors to get the LCM 

LCM(9,12,18) = 36
 

In the division method, 

Step 1: Write the given numbers in a row 

Step 2: proceed with the division of numbers with a factor that is divisible by at least one of the numbers. 

Step 3: Carry forward the numbers that haven’t been divided earlier. 

Step 4: Continue dividing till the remainder is 1 for all the numbers. 

Step 5: Multiply the divisors in the first column to find the LCM. 

Step 6: LCM (9,12,18) = 36 
 

• Multiple — It is a product of a number and any natural integer. So for 18; 18,36,54 are the multiples.

• Prime Factor — It is a prime number that one gets after factorization of any given number. Like for 12; 1,2,3,4,6 and 12 are prime factors as they can be divided by 1 or the number itself.

• Prime Factorization — It is a process of dividing the number into prime factors.

• Co-prime numbers — These are the positive integers, where both the numbers can be divided only by 1. 

• Fraction — It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 18/9– 18 is the numerator and 9 is the denominator. Proper fraction is where numerator is always lesser than denominator.