LCM of 4, 8, and 16
LCM of 4, 8, and 16 is the smallest number among all common multiples of 4, 8, and 16. The first few multiples of 4, 8, and 16 are (4, 8, 12, 16, 20 . . .), (8, 16, 24, 32, 40 . . .), and (16, 32, 48, 64, 80 . . .) respectively. There are 3 commonly used methods to find LCM of 4, 8, 16  by division method, by prime factorization, and by listing multiples.
1.  LCM of 4, 8, and 16 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 4, 8, and 16?
Answer: LCM of 4, 8, and 16 is 16.
Explanation:
The LCM of three nonzero integers, a(4), b(8), and c(16), is the smallest positive integer m(16) that is divisible by a(4), b(8), and c(16) without any remainder.
Methods to Find LCM of 4, 8, and 16
Let's look at the different methods for finding the LCM of 4, 8, and 16.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 4, 8, and 16 by Division Method
To calculate the LCM of 4, 8, and 16 by the division method, we will divide the numbers(4, 8, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 4, 8, and 16.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4, 8, and 16. Write this prime number(2) on the left of the given numbers(4, 8, and 16), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (4, 8, 16) 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 4, 8, and 16 is the product of all prime numbers on the left, i.e. LCM(4, 8, 16) by division method = 2 × 2 × 2 × 2 = 16.
LCM of 4, 8, and 16 by Listing Multiples
To calculate the LCM of 4, 8, 16 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 4 (4, 8, 12, 16, 20 . . .), 8 (8, 16, 24, 32, 40 . . .), and 16 (16, 32, 48, 64, 80 . . .).
 Step 2: The common multiples from the multiples of 4, 8, and 16 are 16, 32, . . .
 Step 3: The smallest common multiple of 4, 8, and 16 is 16.
∴ The least common multiple of 4, 8, and 16 = 16.
LCM of 4, 8, and 16 by Prime Factorization
Prime factorization of 4, 8, and 16 is (2 × 2) = 2^{2}, (2 × 2 × 2) = 2^{3}, and (2 × 2 × 2 × 2) = 2^{4} respectively. LCM of 4, 8, and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} = 16.
Hence, the LCM of 4, 8, and 16 by prime factorization is 16.
ā Also Check:
 LCM of 42 and 63  126
 LCM of 4 and 15  60
 LCM of 8 and 15  120
 LCM of 4 and 13  52
 LCM of 23 and 69  69
 LCM of 7 and 14  14
 LCM of 5, 10, 15 and 20  60
LCM of 4, 8, and 16 Examples

Example 1: Verify the relationship between the GCD and LCM of 4, 8, and 16.
Solution:
The relation between GCD and LCM of 4, 8, and 16 is given as,
LCM(4, 8, 16) = [(4 × 8 × 16) × GCD(4, 8, 16)]/[GCD(4, 8) × GCD(8, 16) × GCD(4, 16)]
⇒ Prime factorization of 4, 8 and 16: 4 = 2^{2}
 8 = 2^{3}
 16 = 2^{4}
∴ GCD of (4, 8), (8, 16), (4, 16) and (4, 8, 16) = 4, 8, 4 and 4 respectively.
Now, LHS = LCM(4, 8, 16) = 16.
And, RHS = [(4 × 8 × 16) × GCD(4, 8, 16)]/[GCD(4, 8) × GCD(8, 16) × GCD(4, 16)] = [(512) × 4]/[4 × 8 × 4] = 16
LHS = RHS = 16.
Hence verified. 
Example 2: Find the smallest number that is divisible by 4, 8, 16 exactly.
Solution:
The smallest number that is divisible by 4, 8, and 16 exactly is their LCM.
⇒ Multiples of 4, 8, and 16: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, . . . .
 Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, . . . .
 Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, . . . .
Therefore, the LCM of 4, 8, and 16 is 16.

Example 3: Calculate the LCM of 4, 8, and 16 using the GCD of the given numbers.
Solution:
Prime factorization of 4, 8, 16:
 4 = 2^{2}
 8 = 2^{3}
 16 = 2^{4}
Therefore, GCD(4, 8) = 4, GCD(8, 16) = 8, GCD(4, 16) = 4, GCD(4, 8, 16) = 4
We know,
LCM(4, 8, 16) = [(4 × 8 × 16) × GCD(4, 8, 16)]/[GCD(4, 8) × GCD(8, 16) × GCD(4, 16)]
LCM(4, 8, 16) = (512 × 4)/(4 × 8 × 4) = 16
⇒LCM(4, 8, 16) = 16
FAQs on LCM of 4, 8, and 16
What is the LCM of 4, 8, and 16?
The LCM of 4, 8, and 16 is 16. To find the LCM (least common multiple) of 4, 8, and 16, we need to find the multiples of 4, 8, and 16 (multiples of 4 = 4, 8, 12 . . . .; multiples of 8 = 8, 16, 24 . . . .; multiples of 16 = 16, 32, 48 . . . .) and choose the smallest multiple that is exactly divisible by 4, 8, and 16, i.e., 16.
What is the Least Perfect Square Divisible by 4, 8, and 16?
The least number divisible by 4, 8, and 16 = LCM(4, 8, 16)
LCM of 4, 8, and 16 = 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 4, 8, and 16 = LCM(4, 8, 16) = 16 [Square root of 16 = √16 = ±4]
Therefore, 16 is the required number.
What is the Relation Between GCF and LCM of 4, 8, 16?
The following equation can be used to express the relation between GCF and LCM of 4, 8, 16, i.e. LCM(4, 8, 16) = [(4 × 8 × 16) × GCF(4, 8, 16)]/[GCF(4, 8) × GCF(8, 16) × GCF(4, 16)].
Which of the following is the LCM of 4, 8, and 16? 5, 105, 16, 2
The value of LCM of 4, 8, 16 is the smallest common multiple of 4, 8, and 16. The number satisfying the given condition is 16.