How to Find LCM of 9 and 12

LCM (Least Common Multiple) of two numbers is the smallest multiple that both numbers can divide evenly without leaving any remainder. In this article, we will learn about LCM, what is LCM of 9 and 12, How to Find LCM of 9 and 12 by Prime Factorization, Listing Multiples, and the division method. We will also look into LCM vs HCF of 9 and 12 in detail.

LCM of 9 and 12

What is LCM of 9 and 12?

Answer: LCM of 9 and 12 is 36

LCM of 9 and 12 is the smallest multiple of 9 and 12 which is common to number and 12. The smallest common multiple of 9 and 12 is 36. Hence, LCM of 9 and 12 is 36. It is the smallest positive number divisible by 9 and 12 without leaving any remainder.

LCM of 9 and 12 Calculator

Try out the following calculator to calculate LCM of 9 and 12

How to Find LCM of 9 and 12?

We can find LCM of 9 and 12 with the following three methods:

• Listing Multiple
• Prime Factorization
• Division

LCM of 9 and 2 By Listing Multiples

In this method we list multiples of 9 and 12. Now, to find LCM we find out the smallest common multiple.

Multiples of 9 are 9, 18, 27, 36, 45, 54…

Multiples of 12 are 12, 24, 36, 48, 60, 72….

Among the multiples of 9 and 12, we find that smallest common multiple is 36. Hence, LCM of 9 and 12 is 36.

LCM of 9 and 12 by Prime Factorization

To find LCM of 9 and 12, follow the steps mentioned below:

• Step 1: Write 9 and 12 as Product of their Prime Factors
• Step 2: Identify the Prime Factors which repeats for highest number of time.
• Step 3: Identify unique prime factors of 9 and 12
• Step 4: Find the product of numbers obtained in step 2 and step 3. This is LCM of 9 and 12.

Following the above steps,

• Prime Factors of 9 = 3 × 3
• Prime Factors of 12 = 2 × 2 × 3

In the above prime factors we find that 2 and 3 is repeated maximum for two times.

Hence, LCM of 9 and 12 is 2 × 2 × 3 × 3 = 36

LCM of 9 and 12 by Division

To find the LCM of 9 and 12 by Division method, use the following steps

• Step 1: Divide the numbers by a number which is a factor of at least two of the numbers.
• Step 2: Write the quotients and carry forward the numbers which are not divisible.
• Step 3: Repeat the steps 1 and 2 till no two of the numbers has a common factor.
• Step 4: The product of the divisors of all the steps and the remaining numbers is the LCM of the numbers.

LCM of 9 and 12 by Long Division is shown below:

LCM of 9 and 12 by Division Method

LCM vs HCF of 9 and 12

LCM is the smallest multiple that both numbers can divide into evenly. For the case of 9 and 12, the LCM would be the smallest number that both 9 and 12 can evenly divide into without the remainder. Hence, LCM of 9 and 12 is 36.

HCF is the biggest number that can divide both 9 and 12, leaving no remainder. Hence, HCF of 9 and 12 is 3.

Examples on LCM of 9 and 12

Example 1: Mihir goes to market after every 9 days and Aman goes to the park after every 12 days. Today both went to the market. After how many days will they both go the market again on the same day?

Solution:

To find out when both Mihir and Aman will go to the market on the same day again, we need to find the least common multiple (LCM) of their visitation intervals.

Mihir’s interval = 9 days

Aman’s interval = 12 days

The LCM of 9 and 12 is 36.

So, after 36 days, they will both go to the market on the same day again.

Example 2: What is the smallest number that leaves a remainder of 2, when it is divided by 9 and 12?

Solution:

To find the smallest number that leaves a remainder of 2 when divided by 9 and 12, we can first find the least common multiple (LCM) of 9 and 12, which is 36.

So, the smallest number that leaves a remainder of 2 when divided by 9 and 12 is 36+2 = 38.

LCM of 9 and 12 Practice Problems

Q1. Find the difference between twice the LCM and the HCF of 9 and 12.

Q2. Find the number when HCF of 9 and 12 subtracted from the LCM.

Q3. If the LCM of 9 and 12 is divided by their HCF, what is the quotient?

Q4. Which of the following is the LCM of 9 and 12?

• 50
• 15
• 45
• 36

LCM of 9 and 12 Frequently Asked Questions

What does LCM stand for?

LCM stands for Least Common Multiple.

How can I find the LCM of 9 and 12?

You can find the LCM of 9 and 12 by listing out their multiples and identifying the smallest number they have in common. Alternatively, you can use methods like prime factorization or long division.

Can you find the LCM of more than two numbers?

Yes, you can find the LCM of more than two numbers. The process is similar to finding the LCM of two numbers, but you’ll need to consider all the numbers involved.

What is the relationship between LCM and HCF?

LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers, while HCF (Highest Common Factor) is the largest number that divides both numbers evenly. The product of LCM and HCF is equal to the product of the two numbers.

Can the LCM of two numbers be smaller than both numbers?

No, the LCM of two numbers must always be greater than or equal to both numbers.

Can LCM be negative?

No, LCM is always a positive number because it represents the smallest positive multiple that two or more numbers share.