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.

Answer: LCM of 3 and 13 is 39.

Explanation:

The LCM of two non-zero 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.

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) = 3¹ and (13) = 13¹ respectively. LCM of 3 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 13¹ = 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

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 = 3¹ × 13¹ = 39.