LCM of 19 and 57

LCM of 19 and 57 is the smallest number among all common multiples of 19 and 57. The first few multiples of 19 and 57 are (19, 38, 57, 76, 95, 114, . . . ) and (57, 114, 171, 228, 285, 342, . . . ) respectively. There are 3 commonly used methods to find LCM of 19 and 57 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 19 and 57 is 57.

Explanation:

The LCM of two non-zero integers, x(19) and y(57), is the smallest positive integer m(57) that is divisible by both x(19) and y(57) without any remainder.

Let's look at the different methods for finding the LCM of 19 and 57.

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

LCM of 19 and 57 by Listing Multiples

To calculate the LCM of 19 and 57 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 57 (57, 114, 171, 228, 285, 342, . . . . )
• Step 2: The common multiples from the multiples of 19 and 57 are 57, 114, . . .
• Step 3: The smallest common multiple of 19 and 57 is 57.

∴ The least common multiple of 19 and 57 = 57.

LCM of 19 and 57 by Prime Factorization

Prime factorization of 19 and 57 is (19) = 19¹ and (3 × 19) = 3¹ × 19¹ respectively. LCM of 19 and 57 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 19¹ = 57.
Hence, the LCM of 19 and 57 by prime factorization is 57.

LCM of 19 and 57 by Division Method

To calculate the LCM of 19 and 57 by the division method, we will divide the numbers(19, 57) by their prime factors (preferably common). The product of these divisors gives the LCM of 19 and 57.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 19 and 57. Write this prime number(3) on the left of the given numbers(19 and 57), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (19, 57) 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 19 and 57 is the product of all prime numbers on the left, i.e. LCM(19, 57) by division method = 3 × 19 = 57.

☛ Also Check:

• LCM of 26 and 91 - 182
• LCM of 6 and 27 - 54
• LCM of 6, 8 and 15 - 120
• LCM of 2, 3 and 6 - 6
• LCM of 13 and 20 - 260
• LCM of 12 and 35 - 420
• LCM of 3 and 6 - 6

FAQs on LCM of 19 and 57

What is the LCM of 19 and 57?

The LCM of 19 and 57 is 57. To find the least common multiple (LCM) of 19 and 57, we need to find the multiples of 19 and 57 (multiples of 19 = 19, 38, 57, 76; multiples of 57 = 57, 114, 171, 228) and choose the smallest multiple that is exactly divisible by 19 and 57, i.e., 57.

What are the Methods to Find LCM of 19 and 57?

The commonly used methods to find the LCM of 19 and 57 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

If the LCM of 57 and 19 is 57, Find its GCF.

LCM(57, 19) × GCF(57, 19) = 57 × 19
Since the LCM of 57 and 19 = 57
⇒ 57 × GCF(57, 19) = 1083
Therefore, the GCF = 1083/57 = 19.

What is the Least Perfect Square Divisible by 19 and 57?

The least number divisible by 19 and 57 = LCM(19, 57)
LCM of 19 and 57 = 3 × 19 [Incomplete pair(s): 3, 19]
⇒ Least perfect square divisible by each 19 and 57 = LCM(19, 57) × 3 × 19 = 3249 [Square root of 3249 = √3249 = ±57]
Therefore, 3249 is the required number.

Which of the following is the LCM of 19 and 57? 18, 57, 45, 25

The value of LCM of 19, 57 is the smallest common multiple of 19 and 57. The number satisfying the given condition is 57.