LCM of 3 and 13
LCM of 3 and 13 is the smallest number among all common multiples of 3 and 13. The first few multiples of 3 and 13 are (3, 6, 9, 12, 15, 18, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 13  by prime factorization, by listing multiples, and by division method.
1.  LCM of 3 and 13 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 3 and 13?
Answer: LCM of 3 and 13 is 39.
Explanation:
The LCM of two nonzero integers, x(3) and y(13), is the smallest positive integer m(39) that is divisible by both x(3) and y(13) without any remainder.
Methods to Find LCM of 3 and 13
The methods to find the LCM of 3 and 13 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 3 and 13 by Division Method
To calculate the LCM of 3 and 13 by the division method, we will divide the numbers(3, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 13.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 13. Write this prime number(3) on the left of the given numbers(3 and 13), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (3, 13) is a multiple of 3, divide it by 3 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 13 is the product of all prime numbers on the left, i.e. LCM(3, 13) by division method = 3 × 13 = 39.
LCM of 3 and 13 by Prime Factorization
Prime factorization of 3 and 13 is (3) = 3^{1} and (13) = 13^{1} respectively. LCM of 3 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{1} × 13^{1} = 39.
Hence, the LCM of 3 and 13 by prime factorization is 39.
LCM of 3 and 13 by Listing Multiples
To calculate the LCM of 3 and 13 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, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
 Step 2: The common multiples from the multiples of 3 and 13 are 39, 78, . . .
 Step 3: The smallest common multiple of 3 and 13 is 39.
∴ The least common multiple of 3 and 13 = 39.
☛ Also Check:
 LCM of 64 and 96  192
 LCM of 48 and 64  192
 LCM of 16 and 30  240
 LCM of 8, 10 and 12  120
 LCM of 11 and 121  121
 LCM of 3, 4 and 9  36
 LCM of 60 and 90  180
LCM of 3 and 13 Examples

Example 1: Verify the relationship between GCF and LCM of 3 and 13.
Solution:
The relation between GCF and LCM of 3 and 13 is given as,
LCM(3, 13) × GCF(3, 13) = Product of 3, 13
Prime factorization of 3 and 13 is given as, 3 = (3) = 3^{1} and 13 = (13) = 13^{1}
LCM(3, 13) = 39
GCF(3, 13) = 1
LHS = LCM(3, 13) × GCF(3, 13) = 39 × 1 = 39
RHS = Product of 3, 13 = 3 × 13 = 39
⇒ LHS = RHS = 39
Hence, verified. 
Example 2: Find the smallest number that is divisible by 3 and 13 exactly.
Solution:
The smallest number that is divisible by 3 and 13 exactly is their LCM.
⇒ Multiples of 3 and 13: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, . . . .
 Multiples of 13 = 13, 26, 39, 52, 65, 78, 91, . . . .
Therefore, the LCM of 3 and 13 is 39.

Example 3: The GCD and LCM of two numbers are 1 and 39 respectively. If one number is 3, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 3 × b
⇒ b = (GCD × LCM)/3
⇒ b = (1 × 39)/3
⇒ b = 13
Therefore, the other number is 13.
FAQs on LCM of 3 and 13
What is the LCM of 3 and 13?
The LCM of 3 and 13 is 39. To find the LCM (least common multiple) of 3 and 13, we need to find the multiples of 3 and 13 (multiples of 3 = 3, 6, 9, 12 . . . . 39; multiples of 13 = 13, 26, 39, 52) and choose the smallest multiple that is exactly divisible by 3 and 13, i.e., 39.
What are the Methods to Find LCM of 3 and 13?
The commonly used methods to find the LCM of 3 and 13 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
Which of the following is the LCM of 3 and 13? 28, 42, 39, 12
The value of LCM of 3, 13 is the smallest common multiple of 3 and 13. The number satisfying the given condition is 39.
If the LCM of 13 and 3 is 39, Find its GCF.
LCM(13, 3) × GCF(13, 3) = 13 × 3
Since the LCM of 13 and 3 = 39
⇒ 39 × GCF(13, 3) = 39
Therefore, the GCF = 39/39 = 1.
How to Find the LCM of 3 and 13 by Prime Factorization?
To find the LCM of 3 and 13 using prime factorization, we will find the prime factors, (3 = 3) and (13 = 13). LCM of 3 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 13.
⇒ LCM of 3, 13 = 3^{1} × 13^{1} = 39.
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