LCM of 15 and 19

LCM of 15 and 19 is the smallest number among all common multiples of 15 and 19. The first few multiples of 15 and 19 are (15, 30, 45, 60, . . . ) and (19, 38, 57, 76, 95, 114, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 19 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 15 and 19 is 285.

Explanation:

The LCM of two non-zero integers, x(15) and y(19), is the smallest positive integer m(285) that is divisible by both x(15) and y(19) without any remainder.

The methods to find the LCM of 15 and 19 are explained below.

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

LCM of 15 and 19 by Listing Multiples

To calculate the LCM of 15 and 19 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 15 (15, 30, 45, 60, . . . ) and 19 (19, 38, 57, 76, 95, 114, . . . . )
• Step 2: The common multiples from the multiples of 15 and 19 are 285, 570, . . .
• Step 3: The smallest common multiple of 15 and 19 is 285.

∴ The least common multiple of 15 and 19 = 285.

LCM of 15 and 19 by Division Method

To calculate the LCM of 15 and 19 by the division method, we will divide the numbers(15, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 19.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 19. Write this prime number(3) on the left of the given numbers(15 and 19), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (15, 19) 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 15 and 19 is the product of all prime numbers on the left, i.e. LCM(15, 19) by division method = 3 × 5 × 19 = 285.

LCM of 15 and 19 by Prime Factorization

Prime factorization of 15 and 19 is (3 × 5) = 3¹ × 5¹ and (19) = 19¹ respectively. LCM of 15 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 19¹ = 285.
Hence, the LCM of 15 and 19 by prime factorization is 285.

☛ Also Check:

• LCM of 4 and 12 - 12
• LCM of 4 and 10 - 20
• LCM of 39 and 65 - 195
• LCM of 37 and 49 - 1813
• LCM of 36 and 90 - 180
• LCM of 36 and 84 - 252
• LCM of 36 and 81 - 324

FAQs on LCM of 15 and 19

What is the LCM of 15 and 19?

The LCM of 15 and 19 is 285. To find the LCM of 15 and 19, we need to find the multiples of 15 and 19 (multiples of 15 = 15, 30, 45, 60 . . . . 285; multiples of 19 = 19, 38, 57, 76 . . . . 285) and choose the smallest multiple that is exactly divisible by 15 and 19, i.e., 285.

If the LCM of 19 and 15 is 285, Find its GCF.

LCM(19, 15) × GCF(19, 15) = 19 × 15
Since the LCM of 19 and 15 = 285
⇒ 285 × GCF(19, 15) = 285
Therefore, the greatest common factor (GCF) = 285/285 = 1.

What is the Relation Between GCF and LCM of 15, 19?

The following equation can be used to express the relation between GCF and LCM of 15 and 19, i.e. GCF × LCM = 15 × 19.

How to Find the LCM of 15 and 19 by Prime Factorization?

To find the LCM of 15 and 19 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (19 = 19). LCM of 15 and 19 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 19.
⇒ LCM of 15, 19 = 3¹ × 5¹ × 19¹ = 285.

What are the Methods to Find LCM of 15 and 19?

The commonly used methods to find the LCM of 15 and 19 are:

• Division Method
• Listing Multiples
• Prime Factorization Method