LCM of 13 and 15

LCM of 13 and 15 is the smallest number among all common multiples of 13 and 15. The first few multiples of 13 and 15 are (13, 26, 39, 52, . . . ) and (15, 30, 45, 60, 75, 90, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 15 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 13 and 15 is 195.

Explanation:

The LCM of two non-zero integers, x(13) and y(15), is the smallest positive integer m(195) that is divisible by both x(13) and y(15) without any remainder.

The methods to find the LCM of 13 and 15 are explained below.

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

LCM of 13 and 15 by Listing Multiples

To calculate the LCM of 13 and 15 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 15 (15, 30, 45, 60, 75, 90, 105, . . . . )
• Step 2: The common multiples from the multiples of 13 and 15 are 195, 390, . . .
• Step 3: The smallest common multiple of 13 and 15 is 195.

∴ The least common multiple of 13 and 15 = 195.

LCM of 13 and 15 by Division Method

To calculate the LCM of 13 and 15 by the division method, we will divide the numbers(13, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 15. Write this prime number(3) on the left of the given numbers(13 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (13, 15) is a multiple of 3, divide it by 3 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 15 is the product of all prime numbers on the left, i.e. LCM(13, 15) by division method = 3 × 5 × 13 = 195.

LCM of 13 and 15 by Prime Factorization

Prime factorization of 13 and 15 is (13) = 13¹ and (3 × 5) = 3¹ × 5¹ respectively. LCM of 13 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 13¹ = 195.
Hence, the LCM of 13 and 15 by prime factorization is 195.

☛ Also Check:

• LCM of 20, 25 and 30 - 300
• LCM of 2, 6 and 8 - 24
• LCM of 2, 5 and 8 - 40
• LCM of 2, 5 and 7 - 70
• LCM of 2, 5 and 6 - 30
• LCM of 2, 5 and 10 - 10
• LCM of 2, 4 and 8 - 8

FAQs on LCM of 13 and 15

What is the LCM of 13 and 15?

The LCM of 13 and 15 is 195. To find the LCM (least common multiple) of 13 and 15, we need to find the multiples of 13 and 15 (multiples of 13 = 13, 26, 39, 52 . . . . 195; multiples of 15 = 15, 30, 45, 60 . . . . 195) and choose the smallest multiple that is exactly divisible by 13 and 15, i.e., 195.

What is the Least Perfect Square Divisible by 13 and 15?

The least number divisible by 13 and 15 = LCM(13, 15)
LCM of 13 and 15 = 3 × 5 × 13 [Incomplete pair(s): 3, 5, 13]
⇒ Least perfect square divisible by each 13 and 15 = LCM(13, 15) × 3 × 5 × 13 = 38025 [Square root of 38025 = √38025 = ±195]
Therefore, 38025 is the required number.

If the LCM of 15 and 13 is 195, Find its GCF.

LCM(15, 13) × GCF(15, 13) = 15 × 13
Since the LCM of 15 and 13 = 195
⇒ 195 × GCF(15, 13) = 195
Therefore, the GCF = 195/195 = 1.

What are the Methods to Find LCM of 13 and 15?

The commonly used methods to find the LCM of 13 and 15 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

Which of the following is the LCM of 13 and 15? 5, 195, 25, 24

The value of LCM of 13, 15 is the smallest common multiple of 13 and 15. The number satisfying the given condition is 195.