LCM of 8 and 13

LCM of 8 and 13 is the smallest number among all common multiples of 8 and 13. The first few multiples of 8 and 13 are (8, 16, 24, 32, 40, 48, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 13 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 8 and 13 is 104.

Explanation:

The LCM of two non-zero integers, x(8) and y(13), is the smallest positive integer m(104) that is divisible by both x(8) and y(13) without any remainder.

The methods to find the LCM of 8 and 13 are explained below.

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

LCM of 8 and 13 by Prime Factorization

Prime factorization of 8 and 13 is (2 × 2 × 2) = 2³ and (13) = 13¹ respectively. LCM of 8 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 13¹ = 104.
Hence, the LCM of 8 and 13 by prime factorization is 104.

LCM of 8 and 13 by Division Method

To calculate the LCM of 8 and 13 by the division method, we will divide the numbers(8, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 13.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 13. Write this prime number(2) on the left of the given numbers(8 and 13), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 13 is the product of all prime numbers on the left, i.e. LCM(8, 13) by division method = 2 × 2 × 2 × 13 = 104.

LCM of 8 and 13 by Listing Multiples

To calculate the LCM of 8 and 13 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
• Step 2: The common multiples from the multiples of 8 and 13 are 104, 208, . . .
• Step 3: The smallest common multiple of 8 and 13 is 104.

∴ The least common multiple of 8 and 13 = 104.

☛ Also Check:

• LCM of 5 and 25 - 25
• LCM of 16 and 28 - 112
• LCM of 4, 5 and 10 - 20
• LCM of 2, 5 and 7 - 70
• LCM of 8, 9 and 10 - 360
• LCM of 1 and 2 - 2
• LCM of 5, 10, 15 and 30 - 30

FAQs on LCM of 8 and 13

What is the LCM of 8 and 13?

The LCM of 8 and 13 is 104. To find the least common multiple (LCM) of 8 and 13, we need to find the multiples of 8 and 13 (multiples of 8 = 8, 16, 24, 32 . . . . 104; multiples of 13 = 13, 26, 39, 52 . . . . 104) and choose the smallest multiple that is exactly divisible by 8 and 13, i.e., 104.

What is the Least Perfect Square Divisible by 8 and 13?

The least number divisible by 8 and 13 = LCM(8, 13)
LCM of 8 and 13 = 2 × 2 × 2 × 13 [Incomplete pair(s): 2, 13]
⇒ Least perfect square divisible by each 8 and 13 = LCM(8, 13) × 2 × 13 = 2704 [Square root of 2704 = √2704 = ±52]
Therefore, 2704 is the required number.

If the LCM of 13 and 8 is 104, Find its GCF.

LCM(13, 8) × GCF(13, 8) = 13 × 8
Since the LCM of 13 and 8 = 104
⇒ 104 × GCF(13, 8) = 104
Therefore, the greatest common factor = 104/104 = 1.

How to Find the LCM of 8 and 13 by Prime Factorization?

To find the LCM of 8 and 13 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (13 = 13). LCM of 8 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 13.
⇒ LCM of 8, 13 = 2³ × 13¹ = 104.

What is the Relation Between GCF and LCM of 8, 13?

The following equation can be used to express the relation between GCF and LCM of 8 and 13, i.e. GCF × LCM = 8 × 13.