LCM of 13 and 14

LCM of 13 and 14 is the smallest number among all common multiples of 13 and 14. The first few multiples of 13 and 14 are (13, 26, 39, 52, . . . ) and (14, 28, 42, 56, 70, 84, 98, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 14 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 13 and 14 is 182.

Explanation:

The LCM of two non-zero integers, x(13) and y(14), is the smallest positive integer m(182) that is divisible by both x(13) and y(14) without any remainder.

The methods to find the LCM of 13 and 14 are explained below.

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

LCM of 13 and 14 by Division Method

To calculate the LCM of 13 and 14 by the division method, we will divide the numbers(13, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 14.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 14. Write this prime number(2) on the left of the given numbers(13 and 14), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (13, 14) 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 14 is the product of all prime numbers on the left, i.e. LCM(13, 14) by division method = 2 × 7 × 13 = 182.

LCM of 13 and 14 by Prime Factorization

Prime factorization of 13 and 14 is (13) = 13¹ and (2 × 7) = 2¹ × 7¹ respectively. LCM of 13 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 7¹ × 13¹ = 182.
Hence, the LCM of 13 and 14 by prime factorization is 182.

LCM of 13 and 14 by Listing Multiples

To calculate the LCM of 13 and 14 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, . . . ) and 14 (14, 28, 42, 56, 70, 84, 98, . . . . )
• Step 2: The common multiples from the multiples of 13 and 14 are 182, 364, . . .
• Step 3: The smallest common multiple of 13 and 14 is 182.

∴ The least common multiple of 13 and 14 = 182.

☛ Also Check:

• LCM of 24, 36 and 40 - 360
• LCM of 24, 36 and 72 - 72
• LCM of 24, 36 and 54 - 216
• LCM of 24, 15 and 36 - 360
• LCM of 20, 40 and 60 - 120
• LCM of 20, 30 and 60 - 60
• LCM of 20, 30 and 40 - 120

FAQs on LCM of 13 and 14

What is the LCM of 13 and 14?

The LCM of 13 and 14 is 182. To find the least common multiple of 13 and 14, we need to find the multiples of 13 and 14 (multiples of 13 = 13, 26, 39, 52 . . . . 182; multiples of 14 = 14, 28, 42, 56 . . . . 182) and choose the smallest multiple that is exactly divisible by 13 and 14, i.e., 182.

What is the Least Perfect Square Divisible by 13 and 14?

The least number divisible by 13 and 14 = LCM(13, 14)
LCM of 13 and 14 = 2 × 7 × 13 [Incomplete pair(s): 2, 7, 13]
⇒ Least perfect square divisible by each 13 and 14 = LCM(13, 14) × 2 × 7 × 13 = 33124 [Square root of 33124 = √33124 = ±182]
Therefore, 33124 is the required number.

What is the Relation Between GCF and LCM of 13, 14?

The following equation can be used to express the relation between GCF and LCM of 13 and 14, i.e. GCF × LCM = 13 × 14.

If the LCM of 14 and 13 is 182, Find its GCF.

LCM(14, 13) × GCF(14, 13) = 14 × 13
Since the LCM of 14 and 13 = 182
⇒ 182 × GCF(14, 13) = 182
Therefore, the greatest common factor = 182/182 = 1.

Which of the following is the LCM of 13 and 14? 28, 24, 2, 182

The value of LCM of 13, 14 is the smallest common multiple of 13 and 14. The number satisfying the given condition is 182.