LCM of 13 and 16
LCM of 13 and 16 is the smallest number among all common multiples of 13 and 16. The first few multiples of 13 and 16 are (13, 26, 39, 52, 65, . . . ) and (16, 32, 48, 64, 80, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 16  by listing multiples, by division method, and by prime factorization.
1.  LCM of 13 and 16 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 13 and 16?
Answer: LCM of 13 and 16 is 208.
Explanation:
The LCM of two nonzero integers, x(13) and y(16), is the smallest positive integer m(208) that is divisible by both x(13) and y(16) without any remainder.
Methods to Find LCM of 13 and 16
Let's look at the different methods for finding the LCM of 13 and 16.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 13 and 16 by Prime Factorization
Prime factorization of 13 and 16 is (13) = 13^{1} and (2 × 2 × 2 × 2) = 2^{4} respectively. LCM of 13 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 13^{1} = 208.
Hence, the LCM of 13 and 16 by prime factorization is 208.
LCM of 13 and 16 by Division Method
To calculate the LCM of 13 and 16 by the division method, we will divide the numbers(13, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 16.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 16. Write this prime number(2) on the left of the given numbers(13 and 16), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (13, 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 13 and 16 is the product of all prime numbers on the left, i.e. LCM(13, 16) by division method = 2 × 2 × 2 × 2 × 13 = 208.
LCM of 13 and 16 by Listing Multiples
To calculate the LCM of 13 and 16 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 13 (13, 26, 39, 52, 65, . . . ) and 16 (16, 32, 48, 64, 80, . . . . )
 Step 2: The common multiples from the multiples of 13 and 16 are 208, 416, . . .
 Step 3: The smallest common multiple of 13 and 16 is 208.
∴ The least common multiple of 13 and 16 = 208.
☛ Also Check:
 LCM of 2, 4 and 7  28
 LCM of 2, 4 and 6  12
 LCM of 2, 4 and 5  20
 LCM of 2, 3 and 7  42
 LCM of 2, 3 and 6  6
 LCM of 2, 3 and 5  30
 LCM of 2, 3 and 4  12
LCM of 13 and 16 Examples

Example 1: Find the smallest number that is divisible by 13 and 16 exactly.
Solution:
The value of LCM(13, 16) will be the smallest number that is exactly divisible by 13 and 16.
⇒ Multiples of 13 and 16: Multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, . . . ., 182, 195, 208, . . . .
 Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 144, 160, 176, 192, 208, . . . .
Therefore, the LCM of 13 and 16 is 208.

Example 2: The GCD and LCM of two numbers are 1 and 208 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 × 208)/16
⇒ a = 13
Therefore, the other number is 13. 
Example 3: Verify the relationship between GCF and LCM of 13 and 16.
Solution:
The relation between GCF and LCM of 13 and 16 is given as,
LCM(13, 16) × GCF(13, 16) = Product of 13, 16
Prime factorization of 13 and 16 is given as, 13 = (13) = 13^{1} and 16 = (2 × 2 × 2 × 2) = 2^{4}
LCM(13, 16) = 208
GCF(13, 16) = 1
LHS = LCM(13, 16) × GCF(13, 16) = 208 × 1 = 208
RHS = Product of 13, 16 = 13 × 16 = 208
⇒ LHS = RHS = 208
Hence, verified.
FAQs on LCM of 13 and 16
What is the LCM of 13 and 16?
The LCM of 13 and 16 is 208. To find the least common multiple of 13 and 16, we need to find the multiples of 13 and 16 (multiples of 13 = 13, 26, 39, 52 . . . . 208; multiples of 16 = 16, 32, 48, 64 . . . . 208) and choose the smallest multiple that is exactly divisible by 13 and 16, i.e., 208.
If the LCM of 16 and 13 is 208, Find its GCF.
LCM(16, 13) × GCF(16, 13) = 16 × 13
Since the LCM of 16 and 13 = 208
⇒ 208 × GCF(16, 13) = 208
Therefore, the GCF = 208/208 = 1.
What is the Least Perfect Square Divisible by 13 and 16?
The least number divisible by 13 and 16 = LCM(13, 16)
LCM of 13 and 16 = 2 × 2 × 2 × 2 × 13 [Incomplete pair(s): 13]
⇒ Least perfect square divisible by each 13 and 16 = LCM(13, 16) × 13 = 2704 [Square root of 2704 = √2704 = ±52]
Therefore, 2704 is the required number.
How to Find the LCM of 13 and 16 by Prime Factorization?
To find the LCM of 13 and 16 using prime factorization, we will find the prime factors, (13 = 13) and (16 = 2 × 2 × 2 × 2). LCM of 13 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 13 and 16.
⇒ LCM of 13, 16 = 2^{4} × 13^{1} = 208.
Which of the following is the LCM of 13 and 16? 208, 24, 20, 30
The value of LCM of 13, 16 is the smallest common multiple of 13 and 16. The number satisfying the given condition is 208.
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