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144 LearnersLast updated on November 29th, 2024
LCM of 9,12 and 18
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.
What is the LCM of 9,12 and 18?
The LCM of 9,12 and 18 is 36. How did we find this?
Let us learn!
How to find the LCM of 9,12 and 18?
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;
LCM of 9,12 and 18 using the Division method
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
LCM of 9,12 and 18 using the prime factorization method
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
LCM of 9,12 and 18 using the division method
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
Common mistakes and how to avoid them in LCM of 9,12 and 18
LCM of 9,12 and 18 Examples
Problem 1
LCM(9,12) = 36, LCM (9,12,x) is also 36. Find x.
Explanation
Problem 2
Find x, LCM (99,12,x) = 36.
Explanation
Problem 3
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).
Explanation
FAQs on the LCM of 9,12 and 18
1.What is the LCM of 9,12,18,36?
2.What is the LCM of 9,12,18, 24 and 27?
3.What is the HCF of 9,12,18 and 21?
4.What is the LCM of 9,12 and 15?
5.What is the GCF of 15 and 60?
Important glossaries for the LCM of 9,12 and 18
- 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.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
