LCM of 4 and 13

LCM of 4 and 13 is the smallest number among all common multiples of 4 and 13. The first few multiples of 4 and 13 are (4, 8, 12, 16, . . . ) and (13, 26, 39, 52, 65, 78, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 13 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 4 and 13 is 52.

Explanation:

The LCM of two non-zero integers, x(4) and y(13), is the smallest positive integer m(52) that is divisible by both x(4) and y(13) without any remainder.

The methods to find the LCM of 4 and 13 are explained below.

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

LCM of 4 and 13 by Division Method

To calculate the LCM of 4 and 13 by the division method, we will divide the numbers(4, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 13.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 13. Write this prime number(2) on the left of the given numbers(4 and 13), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 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 4 and 13 is the product of all prime numbers on the left, i.e. LCM(4, 13) by division method = 2 × 2 × 13 = 52.

LCM of 4 and 13 by Listing Multiples

To calculate the LCM of 4 and 13 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, . . . ) and 13 (13, 26, 39, 52, 65, 78, . . . . )
• Step 2: The common multiples from the multiples of 4 and 13 are 52, 104, . . .
• Step 3: The smallest common multiple of 4 and 13 is 52.

∴ The least common multiple of 4 and 13 = 52.

LCM of 4 and 13 by Prime Factorization

Prime factorization of 4 and 13 is (2 × 2) = 2² and (13) = 13¹ respectively. LCM of 4 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 13¹ = 52.
Hence, the LCM of 4 and 13 by prime factorization is 52.

☛ Also Check:

• LCM of 3, 6 and 12 - 12
• LCM of 3, 4, 5 and 6 - 60
• LCM of 5 and 7 - 35
• LCM of 6 and 7 - 42
• LCM of 12, 16, 24 and 36 - 144
• LCM of 24 and 28 - 168
• LCM of 20 and 50 - 100

FAQs on LCM of 4 and 13

What is the LCM of 4 and 13?

The LCM of 4 and 13 is 52. To find the LCM (least common multiple) of 4 and 13, we need to find the multiples of 4 and 13 (multiples of 4 = 4, 8, 12, 16 . . . . 52; multiples of 13 = 13, 26, 39, 52) and choose the smallest multiple that is exactly divisible by 4 and 13, i.e., 52.

If the LCM of 13 and 4 is 52, Find its GCF.

LCM(13, 4) × GCF(13, 4) = 13 × 4
Since the LCM of 13 and 4 = 52
⇒ 52 × GCF(13, 4) = 52
Therefore, the greatest common factor (GCF) = 52/52 = 1.

How to Find the LCM of 4 and 13 by Prime Factorization?

To find the LCM of 4 and 13 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (13 = 13). LCM of 4 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 13.
⇒ LCM of 4, 13 = 2² × 13¹ = 52.

Which of the following is the LCM of 4 and 13? 40, 42, 52, 11

The value of LCM of 4, 13 is the smallest common multiple of 4 and 13. The number satisfying the given condition is 52.

What are the Methods to Find LCM of 4 and 13?

The commonly used methods to find the LCM of 4 and 13 are:

• Listing Multiples
• Prime Factorization Method
• Division Method