LCM of 18 and 19 is 342. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 18 and 19, the LCM of 18 and 19 is the smallest number. (18, 36, 54, 72, 90, etc.) and (19, 38, 57, 76, 95, 114, 133, etc.) are the first few multiples of 18 and 19, respectively. The division method, listing multiples, and prime factorization are the three most prevalent methods for calculating the LCM of 18 and 19.
Also read: Least common multiple
What is LCM of 18 and 19?
The answer to this question is 342. The LCM of 18 and 19 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 19, is the smallest positive integer 342 which is divisible by both 18 and 19 with no remainder.
How to Find LCM of 18 and 19?
LCM of 18 and 19 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 19 Using Prime Factorisation Method
The prime factorisation of 18 and 19, respectively, is given by:
18 = (2 × 3 × 3) = 21 × 32 and
(19) = 191
LCM (18, 19) = 342
LCM of 18 and 19 Using Division Method
We’ll divide the numbers (18, 19) by their prime factors to get the LCM of 18 and 19 using the division method (preferably common). The LCM of 18 and 19 is calculated by multiplying these divisors.
| 2 | 18 | 19 |
| 3 | 9 | 19 |
| 3 | 3 | 19 |
| 19 | 1 | 19 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (18, 19) = 342
LCM of 18 and 19 Using Listing the Multiples
To calculate the LCM of 18 and 19 by listing out the common multiples, list the multiples as shown below
| Multiples of 18 | Multiples of 19 |
| 18 | 19 |
| 36 | 38 |
| 54 | 57 |
| ……. | …… |
| 342 | 342 |
The smallest common multiple of 18 and 19 is 342.
Therefore LCM (18, 19) = 342
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Video Lesson on Applications of LCM
LCM of 18 and 19 Solved Example
Find the smallest number that is divisible by 18 and 19 exactly.
Solution:
The value of LCM(18, 19) will be the smallest number that is exactly divisible by 18 and 19.
⇒ Multiples of 18 and 19:
Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, . . . ., 306, 324, 342, . . . .
Multiples of 19 = 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, . . . ., 285, 304, 323, 342, . . . .
Therefore, the LCM of 18 and 19 is 342.
Frequently Asked Questions on LCM of 18 and 19
What is the LCM of 18 and 19?
List the methods used to find the LCM of 18 and 19.
What is the Least Perfect Square Divisible by 18 and 19?
LCM of 18 and 19 = 2 × 3 × 3 × 19 [Incomplete pair(s): 2, 19] ⇒ Least perfect square divisible by each 18 and 19 = LCM(18, 19) × 2 × 19 = 12996 [Square root of 12996 = √12996 = ±114] Therefore, 12996 is the required number.
If the LCM of 19 and 18 is 342, Find its GCF.
Since the LCM of 19 and 18 = 342
⇒ 342 × GCF(19, 18) = 342
Therefore, the greatest common factor (GCF) = 342/342 = 1.
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