LCM of 3 and 16
LCM of 3 and 16 is the smallest number among all common multiples of 3 and 16. The first few multiples of 3 and 16 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (16, 32, 48, 64, 80, 96, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 16  by prime factorization, by listing multiples, and by division method.
1.  LCM of 3 and 16 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 3 and 16?
Answer: LCM of 3 and 16 is 48.
Explanation:
The LCM of two nonzero integers, x(3) and y(16), is the smallest positive integer m(48) that is divisible by both x(3) and y(16) without any remainder.
Methods to Find LCM of 3 and 16
The methods to find the LCM of 3 and 16 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 3 and 16 by Prime Factorization
Prime factorization of 3 and 16 is (3) = 3^{1} and (2 × 2 × 2 × 2) = 2^{4} respectively. LCM of 3 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{1} = 48.
Hence, the LCM of 3 and 16 by prime factorization is 48.
LCM of 3 and 16 by Division Method
To calculate the LCM of 3 and 16 by the division method, we will divide the numbers(3, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 16.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 16. Write this prime number(2) on the left of the given numbers(3 and 16), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (3, 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 3 and 16 is the product of all prime numbers on the left, i.e. LCM(3, 16) by division method = 2 × 2 × 2 × 2 × 3 = 48.
LCM of 3 and 16 by Listing Multiples
To calculate the LCM of 3 and 16 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 16 (16, 32, 48, 64, 80, 96, 112, . . . . )
 Step 2: The common multiples from the multiples of 3 and 16 are 48, 96, . . .
 Step 3: The smallest common multiple of 3 and 16 is 48.
∴ The least common multiple of 3 and 16 = 48.
☛ Also Check:
 LCM of 30, 36 and 40  360
 LCM of 28 and 98  196
 LCM of 6 and 7  42
 LCM of 3, 9 and 15  45
 LCM of 12 and 28  84
 LCM of 16 and 36  144
 LCM of 16, 24 and 36  144
LCM of 3 and 16 Examples

Example 1: The product of two numbers is 48. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 48
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 48/1
Therefore, the LCM is 48.
The probable combination for the given case is LCM(3, 16) = 48. 
Example 2: The GCD and LCM of two numbers are 1 and 48 respectively. If one number is 16, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 16 × a
⇒ a = (GCD × LCM)/16
⇒ a = (1 × 48)/16
⇒ a = 3
Therefore, the other number is 3. 
Example 3: Verify the relationship between GCF and LCM of 3 and 16.
Solution:
The relation between GCF and LCM of 3 and 16 is given as,
LCM(3, 16) × GCF(3, 16) = Product of 3, 16
Prime factorization of 3 and 16 is given as, 3 = (3) = 3^{1} and 16 = (2 × 2 × 2 × 2) = 2^{4}
LCM(3, 16) = 48
GCF(3, 16) = 1
LHS = LCM(3, 16) × GCF(3, 16) = 48 × 1 = 48
RHS = Product of 3, 16 = 3 × 16 = 48
⇒ LHS = RHS = 48
Hence, verified.
FAQs on LCM of 3 and 16
What is the LCM of 3 and 16?
The LCM of 3 and 16 is 48. To find the LCM (least common multiple) of 3 and 16, we need to find the multiples of 3 and 16 (multiples of 3 = 3, 6, 9, 12 . . . . 48; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 3 and 16, i.e., 48.
What is the Relation Between GCF and LCM of 3, 16?
The following equation can be used to express the relation between GCF and LCM of 3 and 16, i.e. GCF × LCM = 3 × 16.
Which of the following is the LCM of 3 and 16? 48, 10, 30, 32
The value of LCM of 3, 16 is the smallest common multiple of 3 and 16. The number satisfying the given condition is 48.
How to Find the LCM of 3 and 16 by Prime Factorization?
To find the LCM of 3 and 16 using prime factorization, we will find the prime factors, (3 = 3) and (16 = 2 × 2 × 2 × 2). LCM of 3 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 16.
⇒ LCM of 3, 16 = 2^{4} × 3^{1} = 48.
If the LCM of 16 and 3 is 48, Find its GCF.
LCM(16, 3) × GCF(16, 3) = 16 × 3
Since the LCM of 16 and 3 = 48
⇒ 48 × GCF(16, 3) = 48
Therefore, the greatest common factor (GCF) = 48/48 = 1.
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