LCM of 19 and 38 is 38. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. Among all common multiples of 19 and 38, LCM of 19 and 38 is the smallest number. (19, 38, 57, 76, 95, 114,..) and (38, 76, 114, 152, 190, 228, 266,… ) are the first few multiples of 19 and 38, respectively. Prime factorization, listing multiples, and division are the three most frequent methods for determining the LCM of 19 and 38.
Also read: Least common multiple
What is LCM of 19 and 38?
The answer to this question is 38. The LCM of 19 and 38 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 19 and 38, is the smallest positive integer 38 which is divisible by both 19 and 38 with no remainder.
How to Find LCM of 19 and 38?
LCM of 19 and 38 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 19 and 38 Using Prime Factorisation Method
The prime factorisation of 19 and 38, respectively, is given by:
19 = 191 and
38 = (2 × 19) = 21 × 191
LCM (19, 38) = 38
LCM of 19 and 38 Using Division Method
We’ll divide the numbers (19, 38) by their prime factors to get the LCM of 19 and 38 using the division method (preferably common). The LCM of 19 and 38 is calculated by multiplying these divisors.
| 2 | 19 | 38 |
| 19 | 19 | 19 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (19, 38) = 38
LCM of 19 and 38 Using Listing the Multiples
To calculate the LCM of 19 and 38 by listing out the common multiples, list the multiples as shown below.
| Multiples of 19 | Multiples of 38 |
| 19 | 38 |
| 38 | 76 |
| 57 | 114 |
| 76 | 152 |
| 95 | 190 |
The smallest common multiple of 19 and 38 is 38.
Therefore LCM (19, 38) = 38
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LCM of 19 and 38 Solved Example
Question: The GCD and LCM of two numbers are 19 and 38 respectively. If one number is 19, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 19 × b
⇒ b = (GCD × LCM)/19
⇒ b = (19 × 38)/19
⇒ b = 38
Frequently Asked Questions on LCM of 19 and 38
What is the LCM of 19 and 38?
List the methods used to find the LCM of 19 and 38.
How to Find the LCM of 19 and 38 by Prime Factorization?
⇒ LCM of 19, 38 = 2 × 19 = 38.
Which of the following is the LCM of 19 and 38? 5, 18, 11, 38
If the LCM of 38 and 19 is 38, Find its GCF.
Since the LCM of 38 and 19 = 38
⇒ 38 × GCF(38, 19) = 722
Therefore, the GCF = 722/38 = 19.
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