LCM of 6, 12, 18, and 24
LCM of 6, 12, 18, and 24 is the smallest number among all common multiples of 6, 12, 18, and 24. The first few multiples of 6, 12, 18, and 24 are (6, 12, 18, 24, 30 . . .), (12, 24, 36, 48, 60 . . .), (18, 36, 54, 72, 90 . . .), and (24, 48, 72, 96, 120 . . .) respectively. There are 3 commonly used methods to find LCM of 6, 12, 18, 24  by division method, by listing multiples, and by prime factorization.
1.  LCM of 6, 12, 18, and 24 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 6, 12, 18, and 24?
Answer: LCM of 6, 12, 18, and 24 is 72.
Explanation:
The LCM of four nonzero integers, a(6), b(12), c(18), and d(24), is the smallest positive integer m(72) that is divisible by a(6), b(12), c(18), and d(24) without any remainder.
Methods to Find LCM of 6, 12, 18, and 24
The methods to find the LCM of 6, 12, 18, and 24 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 6, 12, 18, and 24 by Division Method
To calculate the LCM of 6, 12, 18, and 24 by the division method, we will divide the numbers(6, 12, 18, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 6, 12, 18, and 24.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6, 12, 18, and 24. Write this prime number(2) on the left of the given numbers(6, 12, 18, and 24), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (6, 12, 18, 24) 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 6, 12, 18, and 24 is the product of all prime numbers on the left, i.e. LCM(6, 12, 18, 24) by division method = 2 × 2 × 2 × 3 × 3 = 72.
LCM of 6, 12, 18, and 24 by Listing Multiples
To calculate the LCM of 6, 12, 18, 24 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 6 (6, 12, 18, 24, 30 . . .), 12 (12, 24, 36, 48, 60 . . .), 18 (18, 36, 54, 72, 90 . . .), and 24 (24, 48, 72, 96, 120 . . .).
 Step 2: The common multiples from the multiples of 6, 12, 18, and 24 are 72, 144, . . .
 Step 3: The smallest common multiple of 6, 12, 18, and 24 is 72.
∴ The least common multiple of 6, 12, 18, and 24 = 72.
LCM of 6, 12, 18, and 24 by Prime Factorization
Prime factorization of 6, 12, 18, and 24 is (2 × 3) = 2^{1} × 3^{1}, (2 × 2 × 3) = 2^{2} × 3^{1}, (2 × 3 × 3) = 2^{1} × 3^{2}, and (2 × 2 × 2 × 3) = 2^{3} × 3^{1} respectively. LCM of 6, 12, 18, and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{2} = 72.
Hence, the LCM of 6, 12, 18, and 24 by prime factorization is 72.
ā Also Check:
 LCM of 35 and 60  420
 LCM of 12, 16, 24 and 36  144
 LCM of 16, 24 and 40  240
 LCM of 9 and 18  18
 LCM of 24 and 26  312
 LCM of 14 and 24  168
 LCM of 63 and 21  63
LCM of 6, 12, 18, and 24 Examples

Example 1: Which of the following is the LCM of 6, 12, 18, 24? 21, 100, 42, 72.
Solution:
The value of LCM of 6, 12, 18, and 24 is the smallest common multiple of 6, 12, 18, and 24. The number satisfying the given condition is 72. ∴LCM(6, 12, 18, 24) = 72.

Example 2: Find the smallest number that is divisible by 6, 12, 18, 24 exactly.
Solution:
The smallest number that is divisible by 6, 12, 18, and 24 exactly is their LCM.
⇒ Multiples of 6, 12, 18, and 24: Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, . . . .
 Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, . . . .
 Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . . .
 Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, . . . .
Therefore, the LCM of 6, 12, 18, and 24 is 72.

Example 3: Find the smallest number which when divided by 6, 12, 18, and 24 leaves 1 as the remainder in each case.
Solution:
The smallest number exactly divisible by 6, 12, 18, and 24 = LCM(6, 12, 18, 24) ⇒ Smallest number which leaves 1 as remainder when divided by 6, 12, 18, and 24 = LCM(6, 12, 18, 24) + 1
 6 = 2^{1} × 3^{1}
 12 = 2^{2} × 3^{1}
 18 = 2^{1} × 3^{2}
 24 = 2^{3} × 3^{1}
LCM(6, 12, 18, 24) = 2^{3} × 3^{2} = 72
⇒ The required number = 72 + 1 = 73.
FAQs on LCM of 6, 12, 18, and 24
What is the LCM of 6, 12, 18, and 24?
The LCM of 6, 12, 18, and 24 is 72. To find the LCM of 6, 12, 18, and 24, we need to find the multiples of 6, 12, 18, and 24 (multiples of 6 = 6, 12, 18, 24 . . . . 72 . . . . ; multiples of 12 = 12, 24, 36, 48, 72 . . . .; multiples of 18 = 18, 36, 54, 72 . . . .; multiples of 24 = 24, 48, 72, 96 . . . .) and choose the smallest multiple that is exactly divisible by 6, 12, 18, and 24, i.e., 72.
What is the Least Perfect Square Divisible by 6, 12, 18, and 24?
The least number divisible by 6, 12, 18, and 24 = LCM(6, 12, 18, 24)
LCM of 6, 12, 18, and 24 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 6, 12, 18, and 24 = LCM(6, 12, 18, 24) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.
What are the Methods to Find LCM of 6, 12, 18, 24?
The commonly used methods to find the LCM of 6, 12, 18, 24 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
Which of the following is the LCM of 6, 12, 18, and 24? 32, 81, 10, 72
The value of LCM of 6, 12, 18, 24 is the smallest common multiple of 6, 12, 18, and 24. The number satisfying the given condition is 72.
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