LCM of 4 and 26

LCM of 4 and 26 is the smallest number among all common multiples of 4 and 26. The first few multiples of 4 and 26 are (4, 8, 12, 16, 20, . . . ) and (26, 52, 78, 104, 130, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 26 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 4 and 26 is 52.

Explanation:

The LCM of two non-zero integers, x(4) and y(26), is the smallest positive integer m(52) that is divisible by both x(4) and y(26) without any remainder.

The methods to find the LCM of 4 and 26 are explained below.

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

LCM of 4 and 26 by Division Method

To calculate the LCM of 4 and 26 by the division method, we will divide the numbers(4, 26) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 26.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 26. Write this prime number(2) on the left of the given numbers(4 and 26), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 26) 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 26 is the product of all prime numbers on the left, i.e. LCM(4, 26) by division method = 2 × 2 × 13 = 52.

LCM of 4 and 26 by Prime Factorization

Prime factorization of 4 and 26 is (2 × 2) = 2² and (2 × 13) = 2¹ × 13¹ respectively. LCM of 4 and 26 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 13¹ = 52.
Hence, the LCM of 4 and 26 by prime factorization is 52.

LCM of 4 and 26 by Listing Multiples

To calculate the LCM of 4 and 26 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, 20, . . . ) and 26 (26, 52, 78, 104, 130, . . . . )
• Step 2: The common multiples from the multiples of 4 and 26 are 52, 104, . . .
• Step 3: The smallest common multiple of 4 and 26 is 52.

∴ The least common multiple of 4 and 26 = 52.

☛ Also Check:

• LCM of 3, 4 and 5 - 60
• LCM of 16 and 30 - 240
• LCM of 6, 72 and 120 - 360
• LCM of 20 and 32 - 160
• LCM of 4, 12 and 16 - 48
• LCM of 10, 15 and 20 - 60
• LCM of 4 and 22 - 44

FAQs on LCM of 4 and 26

What is the LCM of 4 and 26?

The LCM of 4 and 26 is 52. To find the least common multiple (LCM) of 4 and 26, we need to find the multiples of 4 and 26 (multiples of 4 = 4, 8, 12, 16 . . . . 52; multiples of 26 = 26, 52, 78, 104) and choose the smallest multiple that is exactly divisible by 4 and 26, i.e., 52.

How to Find the LCM of 4 and 26 by Prime Factorization?

To find the LCM of 4 and 26 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (26 = 2 × 13). LCM of 4 and 26 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 26.
⇒ LCM of 4, 26 = 2² × 13¹ = 52.

If the LCM of 26 and 4 is 52, Find its GCF.

LCM(26, 4) × GCF(26, 4) = 26 × 4
Since the LCM of 26 and 4 = 52
⇒ 52 × GCF(26, 4) = 104
Therefore, the greatest common factor (GCF) = 104/52 = 2.

What are the Methods to Find LCM of 4 and 26?

The commonly used methods to find the LCM of 4 and 26 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 4 and 26?

The least number divisible by 4 and 26 = LCM(4, 26)
LCM of 4 and 26 = 2 × 2 × 13 [Incomplete pair(s): 13]
⇒ Least perfect square divisible by each 4 and 26 = LCM(4, 26) × 13 = 676 [Square root of 676 = √676 = ±26]
Therefore, 676 is the required number.