LCM of 6 and 13

LCM of 6 and 13 is the smallest number among all common multiples of 6 and 13. The first few multiples of 6 and 13 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (13, 26, 39, 52, 65, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 13 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 6 and 13 is 78.

Explanation:

The LCM of two non-zero integers, x(6) and y(13), is the smallest positive integer m(78) that is divisible by both x(6) and y(13) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 13.

• By Listing Multiples
• By Division Method
• By Prime Factorization Method

LCM of 6 and 13 by Listing Multiples

To calculate the LCM of 6 and 13 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . ) and 13 (13, 26, 39, 52, 65, . . . . )
• Step 2: The common multiples from the multiples of 6 and 13 are 78, 156, . . .
• Step 3: The smallest common multiple of 6 and 13 is 78.

∴ The least common multiple of 6 and 13 = 78.

LCM of 6 and 13 by Division Method

To calculate the LCM of 6 and 13 by the division method, we will divide the numbers(6, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 13.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 13. Write this prime number(2) on the left of the given numbers(6 and 13), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 13) 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 6 and 13 is the product of all prime numbers on the left, i.e. LCM(6, 13) by division method = 2 × 3 × 13 = 78.

LCM of 6 and 13 by Prime Factorization

Prime factorization of 6 and 13 is (2 × 3) = 2¹ × 3¹ and (13) = 13¹ respectively. LCM of 6 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 13¹ = 78.
Hence, the LCM of 6 and 13 by prime factorization is 78.

☛ Also Check:

• LCM of 12, 16 and 24 - 48
• LCM of 12 and 40 - 120
• LCM of 20, 30 and 40 - 120
• LCM of 24 and 48 - 48
• LCM of 25, 40 and 60 - 600
• LCM of 7 and 11 - 77
• LCM of 30 and 90 - 90

FAQs on LCM of 6 and 13

What is the LCM of 6 and 13?

The LCM of 6 and 13 is 78. To find the LCM of 6 and 13, we need to find the multiples of 6 and 13 (multiples of 6 = 6, 12, 18, 24 . . . . 78; multiples of 13 = 13, 26, 39, 52 . . . . 78) and choose the smallest multiple that is exactly divisible by 6 and 13, i.e., 78.

What are the Methods to Find LCM of 6 and 13?

The commonly used methods to find the LCM of 6 and 13 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

What is the Relation Between GCF and LCM of 6, 13?

The following equation can be used to express the relation between GCF and LCM of 6 and 13, i.e. GCF × LCM = 6 × 13.

If the LCM of 13 and 6 is 78, Find its GCF.

LCM(13, 6) × GCF(13, 6) = 13 × 6
Since the LCM of 13 and 6 = 78
⇒ 78 × GCF(13, 6) = 78
Therefore, the GCF = 78/78 = 1.

How to Find the LCM of 6 and 13 by Prime Factorization?

To find the LCM of 6 and 13 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (13 = 13). LCM of 6 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 13.
⇒ LCM of 6, 13 = 2¹ × 3¹ × 13¹ = 78.