378 LearnersLast updated on May 26th, 2025
LCM of 9 and 12
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 9 and 12. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 9 and 12?
The LCM of 9 and 12 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.
How to find the LCM of 9 and 12 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 9 and 12 using the Listing multiples method
The LCM of 9 and 12 can be found using the following steps;
Steps:
1. Write down the multiples of each number:
Multiples of 9= 9,18,27,36…
Multiples of 12 = 12,24,36…
2. Ascertain the smallest multiple from the listed multiples of 9 and 12.
The LCM (Least common multiple)
The least common multiple of the numbers 9 and 12 is 36.
LCM of 9 and 12 using the Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of the numbers:
Prime factorization of 9 = 3×3
Prime factorization of 12 = 2×2×3
2. Multiply the highest power of each factor ascertained to get the LCM:
LCM (9,12) = 2×2×3×3 = 36
LCM of 9 and 12 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
1. Write down the numbers in a row;
2. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.
3. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
4. The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×2×3×3= 36
LCM (9,12) = 36
Common Mistakes and how to avoid them while finding the LCM of 9 and 12
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 9 and 12, make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 9 and 12.
This can be avoided by always double-checking the multiples of the numbers 9 and 12 and by not stopping too early. To elaborate, listing 9,18 as multiples of 9 and 12,24,36 as multiples of 12 and assuming 9 is the LCM.
LCM of 9 and 12 Examples
Problem 1
Bells at Moonwood High School ring for the assembly, 9 and 12 minutes apart, respectively. If they ring together at 10:00 AM, when will they ring together again?
The LCM of 9 and 12 is 36.
Explanation
The bells will ring together at 10:36 AM next. The LCM of the numbers 9 and 12 is 36, it expresses the smallest common time interval in the given scenario.
Problem 2
The LCM of a and b is 36 and the sum of a and b is 21. Find a and b.
LCM(a, b) = 36
a+b= 21
We know that, LCM(a,b)×HCF(a,b) =a×b
Let us assume that the numbers a and b are 8 and 10,
8+10 = 18, it is not equal to the sum given
Let us assume that the numbers a and b are 9 and 12,
9+12= 21, which is equal to the sum given
Product of 9 and 12;
9 ×12= 108
LCM(a,b)×HCF(a,b) =a×b
LCM(9,12)×HCF(9,12) =9×12
LCM of 9,12;
Prime factorization of 9 = 3×3
Prime factorization of 12 = 2×2×3
LCM(9,12) = 36
HCF of 9,12;
Factors of 9 = 1,3,9
Factors of 12 = 1,2,3,4,6,12
HCF(9,12) = 3
36×3 =9×12
108 =108
Explanation
We, by assuming that a and b are 9 and 12 respectively and verifying the same against the formula figures that the assumption is right and a=9,b=12.
Problem 3
The LCM of 9 and ‘b’ is 36. Ascertain b.
The LCM of a and b can be found using - LCM(a, b) = a×b/HCF(a, b)
We know the LCM(9,b) = 36
and, a = 9
Applying LCM(a, b) = a×b/HCF(a, b)
36 = 9×b/HCF(9, b)
36 = 9×b/3
b= 36×3/9= 12
b= 12
Explanation
The other number, b is 12. We apply the formula as aforementioned to ascertain the missing number.
Problem 4
Two vans arrive at a store every 9 and 12 minutes, respectively, for a delivery. If they both arrive at the station at 8:00 AM, when will they arrive together again?
The LCM of 9 and 12 is 36.
Explanation
The vans will arrive at the station together again in 36 minutes, which will be at 8:36 AM. 36 is the LCM that expresses the smallest common time interval between 9 and 12.
FAQ’s on LCM of 9 and 12
1.Why is the LCM of 9 and 12 not simply their product (9 × 12 = 108) ?
2.What is the relationship between the Highest common factor (HCF) and LCM of 9 and 12?
3.What is the relationship of the LCM and the HCF between the digits 9 and 12? Elaborate using a formula?
4.How can children in Australia use numbers in everyday life to understand LCM of 9 and 12?
5.What are some fun ways kids in Australia can practice LCM of 9 and 12 with numbers?
6.What role do numbers and LCM of 9 and 12 play in helping children in Australia develop problem-solving skills?
7.How can families in Australia create number-rich environments to improve LCM of 9 and 12 skills?
Important glossaries for LCM of 9 and 12
- 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.
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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.
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