LCM of 4 and 16
LCM of 4 and 16 is the smallest number among all common multiples of 4 and 16. The first few multiples of 4 and 16 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (16, 32, 48, 64, 80, 96, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 16  by listing multiples, by division method, and by prime factorization.
1.  LCM of 4 and 16 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 4 and 16?
Answer: LCM of 4 and 16 is 16.
Explanation:
The LCM of two nonzero integers, x(4) and y(16), is the smallest positive integer m(16) that is divisible by both x(4) and y(16) without any remainder.
Methods to Find LCM of 4 and 16
Let's look at the different methods for finding the LCM of 4 and 16.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 4 and 16 by Listing Multiples
To calculate the LCM of 4 and 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, 24, 28, . . . ) and 16 (16, 32, 48, 64, 80, 96, . . . . )
 Step 2: The common multiples from the multiples of 4 and 16 are 16, 32, . . .
 Step 3: The smallest common multiple of 4 and 16 is 16.
∴ The least common multiple of 4 and 16 = 16.
LCM of 4 and 16 by Prime Factorization
Prime factorization of 4 and 16 is (2 × 2) = 2^{2} and (2 × 2 × 2 × 2) = 2^{4} respectively. LCM of 4 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 and 16 by prime factorization is 16.
LCM of 4 and 16 by Division Method
To calculate the LCM of 4 and 16 by the division method, we will divide the numbers(4, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 16.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 16. Write this prime number(2) on the left of the given numbers(4 and 16), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (4, 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 and 16 is the product of all prime numbers on the left, i.e. LCM(4, 16) by division method = 2 × 2 × 2 × 2 = 16.
☛ Also Check:
 LCM of 4 and 14  28
 LCM of 21 and 56  168
 LCM of 5, 8 and 12  120
 LCM of 25 and 60  300
 LCM of 24 and 28  168
 LCM of 15 and 16  240
 LCM of 25 and 36  900
LCM of 4 and 16 Examples

Example 1: The product of two numbers is 64. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 64
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 64/4
Therefore, the LCM is 16.
The probable combination for the given case is LCM(4, 16) = 16. 
Example 2: The GCD and LCM of two numbers are 4 and 16 respectively. If one number is 16, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 16 × p
⇒ p = (GCD × LCM)/16
⇒ p = (4 × 16)/16
⇒ p = 4
Therefore, the other number is 4. 
Example 3: Find the smallest number that is divisible by 4 and 16 exactly.
Solution:
The smallest number that is divisible by 4 and 16 exactly is their LCM.
⇒ Multiples of 4 and 16: Multiples of 4 = 4, 8, 12, 16, 20, . . . .
 Multiples of 16 = 16, 32, 48, 64, 80, . . . .
Therefore, the LCM of 4 and 16 is 16.
FAQs on LCM of 4 and 16
What is the LCM of 4 and 16?
The LCM of 4 and 16 is 16. To find the least common multiple (LCM) of 4 and 16, we need to find the multiples of 4 and 16 (multiples of 4 = 4, 8, 12, 16; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 4 and 16, i.e., 16.
How to Find the LCM of 4 and 16 by Prime Factorization?
To find the LCM of 4 and 16 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (16 = 2 × 2 × 2 × 2). LCM of 4 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 16.
⇒ LCM of 4, 16 = 2^{4} = 16.
What is the Least Perfect Square Divisible by 4 and 16?
The least number divisible by 4 and 16 = LCM(4, 16)
LCM of 4 and 16 = 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 4 and 16 = 16 [Square root of 16 = √16 = ±4]
Therefore, 16 is the required number.
If the LCM of 16 and 4 is 16, Find its GCF.
LCM(16, 4) × GCF(16, 4) = 16 × 4
Since the LCM of 16 and 4 = 16
⇒ 16 × GCF(16, 4) = 64
Therefore, the greatest common factor (GCF) = 64/16 = 4.
What is the Relation Between GCF and LCM of 4, 16?
The following equation can be used to express the relation between GCF and LCM of 4 and 16, i.e. GCF × LCM = 4 × 16.
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