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.
1.  LCM of 19 and 57 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 19 and 57?
Answer: LCM of 19 and 57 is 57.
Explanation:
The LCM of two nonzero 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.
Methods to Find LCM of 19 and 57
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) = 19^{1} and (3 × 19) = 3^{1} × 19^{1} respectively. LCM of 19 and 57 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{1} × 19^{1} = 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
LCM of 19 and 57 Examples

Example 1: The GCD and LCM of two numbers are 19 and 57 respectively. If one number is 19, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 19 × z
⇒ z = (GCD × LCM)/19
⇒ z = (19 × 57)/19
⇒ z = 57
Therefore, the other number is 57. 
Example 2: Find the smallest number that is divisible by 19 and 57 exactly.
Solution:
The smallest number that is divisible by 19 and 57 exactly is their LCM.
⇒ Multiples of 19 and 57: Multiples of 19 = 19, 38, 57, 76, 95, 114, . . . .
 Multiples of 57 = 57, 114, 171, 228, 285, 342, . . . .
Therefore, the LCM of 19 and 57 is 57.

Example 3: Verify the relationship between GCF and LCM of 19 and 57.
Solution:
The relation between GCF and LCM of 19 and 57 is given as,
LCM(19, 57) × GCF(19, 57) = Product of 19, 57
Prime factorization of 19 and 57 is given as, 19 = (19) = 19^{1} and 57 = (3 × 19) = 3^{1} × 19^{1}
LCM(19, 57) = 57
GCF(19, 57) = 19
LHS = LCM(19, 57) × GCF(19, 57) = 57 × 19 = 1083
RHS = Product of 19, 57 = 19 × 57 = 1083
⇒ LHS = RHS = 1083
Hence, verified.
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.