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LCM of 12, 16, 24, and 36

LCM of 12, 16, 24, and 36 is the smallest number among all common multiples of 12, 16, 24, and 36. The first few multiples of 12, 16, 24, and 36 are (12, 24, 36, 48, 60 . . .), (16, 32, 48, 64, 80 . . .), (24, 48, 72, 96, 120 . . .), and (36, 72, 108, 144, 180 . . .) respectively. There are 3 commonly used methods to find LCM of 12, 16, 24, 36 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 12, 16, 24, and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 12, 16, 24, and 36?

Answer: LCM of 12, 16, 24, and 36 is 144.

Explanation:

The LCM of four non-zero integers, a(12), b(16), c(24), and d(36), is the smallest positive integer m(144) that is divisible by a(12), b(16), c(24), and d(36) without any remainder.

Methods to Find LCM of 12, 16, 24, and 36

Let's look at the different methods for finding the LCM of 12, 16, 24, and 36.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 12, 16, 24, and 36 by Prime Factorization

Prime factorization of 12, 16, 24, and 36 is (2 × 2 × 3) = 2² × 3¹, (2 × 2 × 2 × 2) = 2⁴, (2 × 2 × 2 × 3) = 2³ × 3¹, and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 12, 16, 24, and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3² = 144.
Hence, the LCM of 12, 16, 24, and 36 by prime factorization is 144.

LCM of 12, 16, 24, and 36 by Division Method

To calculate the LCM of 12, 16, 24, and 36 by the division method, we will divide the numbers(12, 16, 24, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 12, 16, 24, and 36.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12, 16, 24, and 36. Write this prime number(2) on the left of the given numbers(12, 16, 24, and 36), separated as per the ladder arrangement.
Step 2: If any of the given numbers (12, 16, 24, 36) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 12, 16, 24, and 36 is the product of all prime numbers on the left, i.e. LCM(12, 16, 24, 36) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

LCM of 12, 16, 24, and 36 by Listing Multiples

To calculate the LCM of 12, 16, 24, 36 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 12 (12, 24, 36, 48, 60 . . .), 16 (16, 32, 48, 64, 80 . . .), 24 (24, 48, 72, 96, 120 . . .), and 36 (36, 72, 108, 144, 180 . . .).
Step 2: The common multiples from the multiples of 12, 16, 24, and 36 are 144, 288, . . .
Step 3: The smallest common multiple of 12, 16, 24, and 36 is 144.

∴ The least common multiple of 12, 16, 24, and 36 = 144.

☛ Also Check:

LCM of 12, 16, 24, and 36 Examples

Example 1: Which of the following is the LCM of 12, 16, 24, 36? 81, 52, 144, 10.

Solution:

The value of LCM of 12, 16, 24, and 36 is the smallest common multiple of 12, 16, 24, and 36. The number satisfying the given condition is 144. ∴LCM(12, 16, 24, 36) = 144.
Example 2: Find the smallest number which when divided by 12, 16, 24, and 36 leaves 5 as the remainder in each case.

Solution:

The smallest number exactly divisible by 12, 16, 24, and 36 = LCM(12, 16, 24, 36) ⇒ Smallest number which leaves 5 as remainder when divided by 12, 16, 24, and 36 = LCM(12, 16, 24, 36) + 5
- 12 = 2² × 3¹
- 16 = 2⁴
- 24 = 2³ × 3¹
- 36 = 2² × 3²
LCM(12, 16, 24, 36) = 2⁴ × 3² = 144
⇒ The required number = 144 + 5 = 149.
Example 3: Find the smallest number that is divisible by 12, 16, 24, 36 exactly.

Solution:

The smallest number that is divisible by 12, 16, 24, and 36 exactly is their LCM.
⇒ Multiples of 12, 16, 24, and 36:
- Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, . . . .
- Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, . . . .
- Multiples of 24 = 24, 48, 72, 96, 120, 144, . . . .
- Multiples of 36 = 36, 72, 108, 144, 180, 216, . . . .
Therefore, the LCM of 12, 16, 24, and 36 is 144.

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FAQs on LCM of 12, 16, 24, and 36

What is the LCM of 12, 16, 24, and 36?

The LCM of 12, 16, 24, and 36 is 144. To find the least common multiple (LCM) of 12, 16, 24, and 36, we need to find the multiples of 12, 16, 24, and 36 (multiples of 12 = 12, 24, 36, 48 . . . . 144 . . . . ; multiples of 16 = 16, 32, 48, 64 . . . . 144 . . . . ; multiples of 24 = 24, 48, 72, 96, 144 . . . .; multiples of 36 = 36, 72, 108, 144 . . . .) and choose the smallest multiple that is exactly divisible by 12, 16, 24, and 36, i.e., 144.

What is the Least Perfect Square Divisible by 12, 16, 24, and 36?

The least number divisible by 12, 16, 24, and 36 = LCM(12, 16, 24, 36)
LCM of 12, 16, 24, and 36 = 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 12, 16, 24, and 36 = LCM(12, 16, 24, 36) = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

Which of the following is the LCM of 12, 16, 24, and 36? 42, 120, 144, 15

The value of LCM of 12, 16, 24, 36 is the smallest common multiple of 12, 16, 24, and 36. The number satisfying the given condition is 144.

What are the Methods to Find LCM of 12, 16, 24, 36?

The commonly used methods to find the LCM of 12, 16, 24, 36 are:

Listing Multiples
Prime Factorization Method
Division Method

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