LCM of 12, 18, and 24
LCM of 12, 18, and 24 is the smallest number among all common multiples of 12, 18, and 24. The first few multiples of 12, 18, and 24 are (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 12, 18, 24  by division method, by listing multiples, and by prime factorization.
1.  LCM of 12, 18, and 24 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 12, 18, and 24?
Answer: LCM of 12, 18, and 24 is 72.
Explanation:
The LCM of three nonzero integers, a(12), b(18), and c(24), is the smallest positive integer m(72) that is divisible by a(12), b(18), and c(24) without any remainder.
Methods to Find LCM of 12, 18, and 24
The methods to find the LCM of 12, 18, and 24 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 12, 18, and 24 by Prime Factorization
Prime factorization of 12, 18, and 24 is (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 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 12, 18, and 24 by prime factorization is 72.
LCM of 12, 18, and 24 by Listing Multiples
To calculate the LCM of 12, 18, 24 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 . . .), 18 (18, 36, 54, 72, 90 . . .), and 24 (24, 48, 72, 96, 120 . . .).
 Step 2: The common multiples from the multiples of 12, 18, and 24 are 72, 144, . . .
 Step 3: The smallest common multiple of 12, 18, and 24 is 72.
∴ The least common multiple of 12, 18, and 24 = 72.
LCM of 12, 18, and 24 by Division Method
To calculate the LCM of 12, 18, and 24 by the division method, we will divide the numbers(12, 18, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 12, 18, and 24.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12, 18, and 24. Write this prime number(2) on the left of the given numbers(12, 18, and 24), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (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 12, 18, and 24 is the product of all prime numbers on the left, i.e. LCM(12, 18, 24) by division method = 2 × 2 × 2 × 3 × 3 = 72.
ā Also Check:
 LCM of 12 and 45  180
 LCM of 48, 56 and 72  1008
 LCM of 9 and 27  27
 LCM of 2923 and 3239  119843
 LCM of 84 and 90  1260
 LCM of 3, 4 and 5  60
 LCM of 8, 12 and 15  120
LCM of 12, 18, and 24 Examples

Example 1: Calculate the LCM of 12, 18, and 24 using the GCD of the given numbers.
Solution:
Prime factorization of 12, 18, 24:
 12 = 2^{2} × 3^{1}
 18 = 2^{1} × 3^{2}
 24 = 2^{3} × 3^{1}
Therefore, GCD(12, 18) = 6, GCD(18, 24) = 6, GCD(12, 24) = 12, GCD(12, 18, 24) = 6
We know,
LCM(12, 18, 24) = [(12 × 18 × 24) × GCD(12, 18, 24)]/[GCD(12, 18) × GCD(18, 24) × GCD(12, 24)]
LCM(12, 18, 24) = (5184 × 6)/(6 × 6 × 12) = 72
⇒LCM(12, 18, 24) = 72 
Example 2: Find the smallest number that is divisible by 12, 18, 24 exactly.
Solution:
The smallest number that is divisible by 12, 18, and 24 exactly is their LCM.
⇒ Multiples of 12, 18, and 24: Multiples of 12 = 12, 24, 36, 48, 60, 72, . . . .
 Multiples of 18 = 18, 36, 54, 72, 90, 108, . . . .
 Multiples of 24 = 24, 48, 72, 96, 120, 144, . . . .
Therefore, the LCM of 12, 18, and 24 is 72.

Example 3: Verify the relationship between the GCD and LCM of 12, 18, and 24.
Solution:
The relation between GCD and LCM of 12, 18, and 24 is given as,
LCM(12, 18, 24) = [(12 × 18 × 24) × GCD(12, 18, 24)]/[GCD(12, 18) × GCD(18, 24) × GCD(12, 24)]
⇒ Prime factorization of 12, 18 and 24: 12 = 2^{2} × 3^{1}
 18 = 2^{1} × 3^{2}
 24 = 2^{3} × 3^{1}
∴ GCD of (12, 18), (18, 24), (12, 24) and (12, 18, 24) = 6, 6, 12 and 6 respectively.
Now, LHS = LCM(12, 18, 24) = 72.
And, RHS = [(12 × 18 × 24) × GCD(12, 18, 24)]/[GCD(12, 18) × GCD(18, 24) × GCD(12, 24)] = [(5184) × 6]/[6 × 6 × 12] = 72
LHS = RHS = 72.
Hence verified.
FAQs on LCM of 12, 18, and 24
What is the LCM of 12, 18, and 24?
The LCM of 12, 18, and 24 is 72. To find the LCM of 12, 18, and 24, we need to find the multiples of 12, 18, and 24 (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 12, 18, and 24, i.e., 72.
What are the Methods to Find LCM of 12, 18, 24?
The commonly used methods to find the LCM of 12, 18, 24 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
Which of the following is the LCM of 12, 18, and 24? 16, 40, 72, 11
The value of LCM of 12, 18, 24 is the smallest common multiple of 12, 18, and 24. The number satisfying the given condition is 72.
What is the Relation Between GCF and LCM of 12, 18, 24?
The following equation can be used to express the relation between GCF and LCM of 12, 18, 24, i.e. LCM(12, 18, 24) = [(12 × 18 × 24) × GCF(12, 18, 24)]/[GCF(12, 18) × GCF(18, 24) × GCF(12, 24)].