LCM of 19 and 38

LCM of 19 and 38 is the smallest number among all common multiples of 19 and 38. The first few multiples of 19 and 38 are (19, 38, 57, 76, 95, 114, . . . ) and (38, 76, 114, 152, 190, 228, 266, . . . ) respectively. There are 3 commonly used methods to find LCM of 19 and 38 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 19 and 38 is 38.

Explanation:

The LCM of two non-zero integers, x(19) and y(38), is the smallest positive integer m(38) that is divisible by both x(19) and y(38) without any remainder.

Let's look at the different methods for finding the LCM of 19 and 38.

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

LCM of 19 and 38 by Prime Factorization

Prime factorization of 19 and 38 is (19) = 19¹ and (2 × 19) = 2¹ × 19¹ respectively. LCM of 19 and 38 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 19¹ = 38.
Hence, the LCM of 19 and 38 by prime factorization is 38.

LCM of 19 and 38 by Listing Multiples

To calculate the LCM of 19 and 38 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 19 (19, 38, 57, 76, 95, 114, . . . ) and 38 (38, 76, 114, 152, 190, 228, 266, . . . . )
• Step 2: The common multiples from the multiples of 19 and 38 are 38, 76, . . .
• Step 3: The smallest common multiple of 19 and 38 is 38.

∴ The least common multiple of 19 and 38 = 38.

LCM of 19 and 38 by Division Method

To calculate the LCM of 19 and 38 by the division method, we will divide the numbers(19, 38) by their prime factors (preferably common). The product of these divisors gives the LCM of 19 and 38.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 19 and 38. Write this prime number(2) on the left of the given numbers(19 and 38), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (19, 38) 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 19 and 38 is the product of all prime numbers on the left, i.e. LCM(19, 38) by division method = 2 × 19 = 38.

☛ Also Check:

• LCM of 60, 84 and 108 - 3780
• LCM of 20 and 50 - 100
• LCM of 4, 8, 12 and 24 - 24
• LCM of 2, 4 and 5 - 20
• LCM of 28 and 30 - 420
• LCM of 5, 9 and 15 - 45
• LCM of 14 and 56 - 56

FAQs on LCM of 19 and 38

What is the LCM of 19 and 38?

The LCM of 19 and 38 is 38. To find the least common multiple (LCM) of 19 and 38, we need to find the multiples of 19 and 38 (multiples of 19 = 19, 38, 57, 76; multiples of 38 = 38, 76, 114, 152) and choose the smallest multiple that is exactly divisible by 19 and 38, i.e., 38.

How to Find the LCM of 19 and 38 by Prime Factorization?

To find the LCM of 19 and 38 using prime factorization, we will find the prime factors, (19 = 19) and (38 = 2 × 19). LCM of 19 and 38 is the product of prime factors raised to their respective highest exponent among the numbers 19 and 38.
⇒ LCM of 19, 38 = 2¹ × 19¹ = 38.

Which of the following is the LCM of 19 and 38? 5, 18, 11, 38

The value of LCM of 19, 38 is the smallest common multiple of 19 and 38. The number satisfying the given condition is 38.

What are the Methods to Find LCM of 19 and 38?

The commonly used methods to find the LCM of 19 and 38 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

If the LCM of 38 and 19 is 38, Find its GCF.

LCM(38, 19) × GCF(38, 19) = 38 × 19
Since the LCM of 38 and 19 = 38
⇒ 38 × GCF(38, 19) = 722
Therefore, the GCF = 722/38 = 19.