LCM of 2 and 13

LCM of 2 and 13 is the smallest number among all common multiples of 2 and 13. The first few multiples of 2 and 13 are (2, 4, 6, 8, 10, 12, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 13 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 2 and 13 is 26.

Explanation:

The LCM of two non-zero integers, x(2) and y(13), is the smallest positive integer m(26) that is divisible by both x(2) and y(13) without any remainder.

The methods to find the LCM of 2 and 13 are explained below.

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

LCM of 2 and 13 by Prime Factorization

Prime factorization of 2 and 13 is (2) = 2¹ and (13) = 13¹ respectively. LCM of 2 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 13¹ = 26.
Hence, the LCM of 2 and 13 by prime factorization is 26.

LCM of 2 and 13 by Division Method

To calculate the LCM of 2 and 13 by the division method, we will divide the numbers(2, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 13.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 13. Write this prime number(2) on the left of the given numbers(2 and 13), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (2, 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 2 and 13 is the product of all prime numbers on the left, i.e. LCM(2, 13) by division method = 2 × 13 = 26.

LCM of 2 and 13 by Listing Multiples

To calculate the LCM of 2 and 13 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
• Step 2: The common multiples from the multiples of 2 and 13 are 26, 52, . . .
• Step 3: The smallest common multiple of 2 and 13 is 26.

∴ The least common multiple of 2 and 13 = 26.

☛ Also Check:

• LCM of 9, 12 and 15 - 180
• LCM of 50 and 70 - 350
• LCM of 20, 25 and 30 - 300
• LCM of 15 and 27 - 135
• LCM of 2, 3 and 7 - 42
• LCM of 16, 28 and 40 - 560
• LCM of 63 and 81 - 567

FAQs on LCM of 2 and 13

What is the LCM of 2 and 13?

The LCM of 2 and 13 is 26. To find the LCM of 2 and 13, we need to find the multiples of 2 and 13 (multiples of 2 = 2, 4, 6, 8 . . . . 26; multiples of 13 = 13, 26, 39, 52) and choose the smallest multiple that is exactly divisible by 2 and 13, i.e., 26.

What is the Relation Between GCF and LCM of 2, 13?

The following equation can be used to express the relation between GCF and LCM of 2 and 13, i.e. GCF × LCM = 2 × 13.

Which of the following is the LCM of 2 and 13? 18, 5, 32, 26

The value of LCM of 2, 13 is the smallest common multiple of 2 and 13. The number satisfying the given condition is 26.

If the LCM of 13 and 2 is 26, Find its GCF.

LCM(13, 2) × GCF(13, 2) = 13 × 2
Since the LCM of 13 and 2 = 26
⇒ 26 × GCF(13, 2) = 26
Therefore, the greatest common factor (GCF) = 26/26 = 1.

How to Find the LCM of 2 and 13 by Prime Factorization?

To find the LCM of 2 and 13 using prime factorization, we will find the prime factors, (2 = 2) and (13 = 13). LCM of 2 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 13.
⇒ LCM of 2, 13 = 2¹ × 13¹ = 26.