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Last updated on November 30th, 2024

LCM of 12 and 24

Q: What is the LCM of 12, 24 and 48?

48 as it is the smallest number that is a multiple of all three.

Q: What is the LCM of 12,24 and 60?

120 as it is the smallest number that is a multiple of all three.

Q: What is the HCF of 12, 24 and 30?

6 as it is the largest number that divides all without leaving a remainder.

Q: What is the HCF of 26 and 63?

1 as it is the only common factor, which means that 26 and 63 are relatively prime (they have no other common factors).

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

The least common multiple is defined as the smallest multiple that two or more numbers have in common. LCM has many real-life applications, such as determining the events by finding the LCM or determining the traffic lights to optimize the flow of traffic.

What is the LCM of 12 and 24

The LCM of 12 and 24 is 24 as 24 is the smallest positive integer that is divisible by both 12 and 24 without any remainder.

How to find the LCM of 12 and 24

There are various methods to find the LCM of 12 and 24.

Listing Multiples

Prime Factorization

Division Method

LCM of 12 and 24 Using Listing the Multiples

To calculate the LCM of 12 and 24 using listing multiples, below are the steps to be followed:

Step 1: List a few multiples of 12 and 24

12 - 12, 24, 36, 48, 60……

24 - 24, 48, 72, 96, 120…..

Step 2: From the multiples of 12 and 24, we can see that 24 and 48 are the common multiples of 12 and 24.

Step 3: The smallest common multiple of 12 and 24 is 24

Therefore, the least common multiple of 12 and 24 is 24.

LCM of 12 and 24 Using Prime Factorization

To find the LCM of 12 and 24 using the Prime Factorization method:

Step 1: Find the prime factors of 12 and 24

Prime factors of 12 = 2×2×3 = 2²× 3¹

Prime factors of 24 = 2×2×2×3 = 2³ × 3¹

Step 2: Now multiply prime factors raised to their respective highest power.

i.e., 23 × 31 = 24.

Therefore, the LCM of 12 and 24 is 24

LCM of 12 and 24 Using Division Method

Here are the steps to find the LCM of 12 and 24 using the Division method:

Step 1: Write 12 and 24 in a row

Step 2: Find the smallest prime number that can divide either 12 or 24.

Here 2 is the smallest prime number.

Step 3: Divide and repeat the same process until you can’t divide anymore.

Step 4: After dividing, multiply all the prime numbers you used to divide.

Here, 2×2×3×2 = 24

Therefore, LCM of 12 and 24 is 24.

Common Mistakes and How to Avoid Them in LCM of 12 and 24

LCM of 12 and 24 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

If a Manson has two tasks that take 12 and 24 minutes, respectively, how long will it take to complete both tasks if the Manson does them one after the other?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

If two trains leave the same station, one every 12 minutes and the other every 24 minutes, when will they both leave the station at the same time again after leaving together?

Explanation

Problem 3

A child has 12 red pencils and 24 blue pencils. The child wants to bundle them into equal groups with the same number of pencils of each color. What is the largest number of groups the child can make?

Explanation

FAQs on Least Common Multiple of 12 and 24

1.What is the LCM of 12, 24 and 48?

2.What is the LCM of 12,24 and 60?

3.Is 12 a factor of 24?

4.What is the HCF of 12, 24 and 30?

5.What is the HCF of 26 and 63?

Important Glossaries for LCM of 12 and 24

Prime number: A prime number is a natural number that is greater than 1 and cannot be formed by multiplying two smaller numbers.

Greatest common divisor: It is the largest positive integer that divides two or more integers without leaving a remainder.

Common multiple: A common multiple is a number that is a multiple of two or more numbers.

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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.