Last updated on May 26th, 2025
LCM is applied in most everyday tasks like planning, aligning events and even in alarms which is used literally every day. In this article, let us learn more about the 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;
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
Listed here are a few common mistakes that one may commit while trying to find the LCM of 9,12 and 18, make a note while practicing.
LCM(9,12) = 36, LCM (9,12,x) is also 36. Find x.
The possible values of x could be → 1,2,3,4,6,9,12,18 or 36.
The LCM of the numbers 9 and 12 is 36 and for the LCM to still remain as 36 after a number is included, i.e., 9,12,x; it must be a divisor of the number 36. The possible number of x is going to be a divisor of 36. Therefore, the possible values could be the above listed divisors.
Find x, LCM (99,12,x) = 36.
We know the LCM of 9,12 = 36
Prime factorization of 36 36 = 3×3×2×2
The LCM of 3,9 already includes 32 and 22, and the factor of x must include the same, which means the factors of 36 are likely the value of x → 1,2,3,6,12,18,36.
By following the above assumption we can assume that the value of x is one of 1,2,3,6,12,18,36.
Prove that LCM(a², b²) = LCM(a, b)² in a case where ‘a’ and ‘b’ are co-prime. Apply to find the LCM(9²,12²).
We can tell that 9 and 12 are not coprime, they have more factors than just 1 and themselves. To make it so, we prime factorize them;
9 = 32
12 = 22×3
Now we find their squares;
92 = 34 = 81
122 =24×32 = 144
We now use the formula for prime factors;
LCM(92,122) = LCM(34,24×32)
= 24×34
= 16×81
= 1296
The formula LCM(a2, b2) = LCM(a, b)2 holds good. The LCM of 92 and 122 is 1296.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.