LCM of 14 and 19

LCM of 14 and 19 is the smallest number among all common multiples of 14 and 19. The first few multiples of 14 and 19 are (14, 28, 42, 56, 70, 84, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 19 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 14 and 19 is 266.

Explanation:

The LCM of two non-zero integers, x(14) and y(19), is the smallest positive integer m(266) that is divisible by both x(14) and y(19) without any remainder.

The methods to find the LCM of 14 and 19 are explained below.

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

LCM of 14 and 19 by Listing Multiples

To calculate the LCM of 14 and 19 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 14 (14, 28, 42, 56, 70, 84, . . . ) and 19 (19, 38, 57, 76, 95, . . . . )
• Step 2: The common multiples from the multiples of 14 and 19 are 266, 532, . . .
• Step 3: The smallest common multiple of 14 and 19 is 266.

∴ The least common multiple of 14 and 19 = 266.

LCM of 14 and 19 by Prime Factorization

Prime factorization of 14 and 19 is (2 × 7) = 2¹ × 7¹ and (19) = 19¹ respectively. LCM of 14 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 7¹ × 19¹ = 266.
Hence, the LCM of 14 and 19 by prime factorization is 266.

LCM of 14 and 19 by Division Method

To calculate the LCM of 14 and 19 by the division method, we will divide the numbers(14, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 19.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 19. Write this prime number(2) on the left of the given numbers(14 and 19), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 19) 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 14 and 19 is the product of all prime numbers on the left, i.e. LCM(14, 19) by division method = 2 × 7 × 19 = 266.

☛ Also Check:

• LCM of 9 and 27 - 27
• LCM of 9 and 24 - 72
• LCM of 9 and 21 - 63
• LCM of 9 and 18 - 18
• LCM of 9 and 16 - 144
• LCM of 9 and 15 - 45
• LCM of 9 and 14 - 126

FAQs on LCM of 14 and 19

What is the LCM of 14 and 19?

The LCM of 14 and 19 is 266. To find the LCM (least common multiple) of 14 and 19, we need to find the multiples of 14 and 19 (multiples of 14 = 14, 28, 42, 56 . . . . 266; multiples of 19 = 19, 38, 57, 76 . . . . 266) and choose the smallest multiple that is exactly divisible by 14 and 19, i.e., 266.

If the LCM of 19 and 14 is 266, Find its GCF.

LCM(19, 14) × GCF(19, 14) = 19 × 14
Since the LCM of 19 and 14 = 266
⇒ 266 × GCF(19, 14) = 266
Therefore, the greatest common factor (GCF) = 266/266 = 1.

What is the Least Perfect Square Divisible by 14 and 19?

The least number divisible by 14 and 19 = LCM(14, 19)
LCM of 14 and 19 = 2 × 7 × 19 [Incomplete pair(s): 2, 7, 19]
⇒ Least perfect square divisible by each 14 and 19 = LCM(14, 19) × 2 × 7 × 19 = 70756 [Square root of 70756 = √70756 = ±266]
Therefore, 70756 is the required number.

What are the Methods to Find LCM of 14 and 19?

The commonly used methods to find the LCM of 14 and 19 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

How to Find the LCM of 14 and 19 by Prime Factorization?

To find the LCM of 14 and 19 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (19 = 19). LCM of 14 and 19 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 19.
⇒ LCM of 14, 19 = 2¹ × 7¹ × 19¹ = 266.