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110 Learners

Last updated on ** September 26th, 2024**

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.

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.

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

- Listing Multiples

- Prime Factorization

- Division Method

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.

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 = 2^{2 }× 3^{1 }

Prime factors of 24 = 2×2×2×3 = 2^{3} × 3^{1}

**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

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.

**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.