LCM of 19 and 21 is 399. Students will know the common multiple of 19 and 21 which is the LCM value. By knowing the common multiples, you will be able to find the least common multiple of 19 and 21. (19, 38, 57, 76, 95, 114, 133, ….) and (21, 42, 63, 84, 105,….) are the first few multiples of 19 and 21. To find the LCM value, few methods like prime factorisation, division and listing of multiples can be used.
Also read: Least common multiple
What is LCM of 19 and 21?
The answer to this question is 399. The LCM of 19 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 19 and 21, is the smallest positive integer 399 which is divisible by both 19 and 21 with no remainder.
How to Find LCM of 19 and 21?
LCM of 19 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 19 and 21 Using Prime Factorisation Method
The prime factorisation of 19 and 21, respectively, is given by:
19 = 19¹
21 = 3 × 7 = 3¹ x 7¹
LCM (19, 21) = 399
LCM of 19 and 21 Using Division Method
We’ll divide the numbers (19, 21) by their prime factors to get the LCM of 19 and 21 using the division method (preferably common). The LCM of 19 and 21 is calculated by multiplying these divisors.
|
3 |
19 |
21 |
|
7 |
19 |
7 |
|
19 |
19 |
1 |
|
× |
1 |
1 |
No further division can be done.
Hence, LCM (19, 21) = 399
LCM of 19 and 21 Using Listing the Multiples
To calculate the LCM of 19 and 21 by listing out the common multiples, list the multiples as shown below:
Multiples of 19 = 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, . . . ., 323, 342, 361, 380, 399, . . . .
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 357, 378, 399, . . . .
LCM (19, 21) = 399
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LCM of 19 and 21 Solved Examples
Question: Find the LCM if the product of two numbers is 399 and the GCD is 1.
Solution:
It is given that
Product of two numbers = 399
GCD = 1
We know that,
LCM × GCD = Product of two numbers
LCM = Product/GCD
LCM = 399/1
LCM = 399
Hence, the LCM is 399.
Frequently Asked Questions on LCM of 19 and 21
Find the LCM of 19 and 21.
What methods can be used to find the LCM of 19 and 21?
Find the GCF if the LCM of 19 and 21 is 399.
LCM × GCF = 19 × 21
Given
LCM of 19 and 21 = 399
399 × GCF = 399
GCF = 399/399 = 1
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