LCM of 13 and 52

LCM of 13 and 52 is the smallest number among all common multiples of 13 and 52. The first few multiples of 13 and 52 are (13, 26, 39, 52, 65, 78, 91, . . . ) and (52, 104, 156, 208, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 52 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 13 and 52 is 52.

Explanation:

The LCM of two non-zero integers, x(13) and y(52), is the smallest positive integer m(52) that is divisible by both x(13) and y(52) without any remainder.

The methods to find the LCM of 13 and 52 are explained below.

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

LCM of 13 and 52 by Prime Factorization

Prime factorization of 13 and 52 is (13) = 13¹ and (2 × 2 × 13) = 2² × 13¹ respectively. LCM of 13 and 52 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 13¹ = 52.
Hence, the LCM of 13 and 52 by prime factorization is 52.

LCM of 13 and 52 by Division Method

To calculate the LCM of 13 and 52 by the division method, we will divide the numbers(13, 52) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 52.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 52. Write this prime number(2) on the left of the given numbers(13 and 52), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (13, 52) 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 13 and 52 is the product of all prime numbers on the left, i.e. LCM(13, 52) by division method = 2 × 2 × 13 = 52.

LCM of 13 and 52 by Listing Multiples

To calculate the LCM of 13 and 52 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 13 (13, 26, 39, 52, 65, 78, 91, . . . ) and 52 (52, 104, 156, 208, . . . . )
• Step 2: The common multiples from the multiples of 13 and 52 are 52, 104, . . .
• Step 3: The smallest common multiple of 13 and 52 is 52.

∴ The least common multiple of 13 and 52 = 52.

☛ Also Check:

• LCM of 4, 5 and 10 - 20
• LCM of 30, 45 and 60 - 180
• LCM of 3, 4 and 8 - 24
• LCM of 24, 30 and 40 - 120
• LCM of 8, 12, 15 and 20 - 120
• LCM of 7, 8, 14 and 21 - 168
• LCM of 7, 8, 11 and 12 - 1848

FAQs on LCM of 13 and 52

What is the LCM of 13 and 52?

The LCM of 13 and 52 is 52. To find the LCM of 13 and 52, we need to find the multiples of 13 and 52 (multiples of 13 = 13, 26, 39, 52; multiples of 52 = 52, 104, 156, 208) and choose the smallest multiple that is exactly divisible by 13 and 52, i.e., 52.

How to Find the LCM of 13 and 52 by Prime Factorization?

To find the LCM of 13 and 52 using prime factorization, we will find the prime factors, (13 = 13) and (52 = 2 × 2 × 13). LCM of 13 and 52 is the product of prime factors raised to their respective highest exponent among the numbers 13 and 52.
⇒ LCM of 13, 52 = 2² × 13¹ = 52.

If the LCM of 52 and 13 is 52, Find its GCF.

LCM(52, 13) × GCF(52, 13) = 52 × 13
Since the LCM of 52 and 13 = 52
⇒ 52 × GCF(52, 13) = 676
Therefore, the GCF (greatest common factor) = 676/52 = 13.

What are the Methods to Find LCM of 13 and 52?

The commonly used methods to find the LCM of 13 and 52 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

Which of the following is the LCM of 13 and 52? 42, 27, 45, 52

The value of LCM of 13, 52 is the smallest common multiple of 13 and 52. The number satisfying the given condition is 52.