LCM of 12 and 19 is 228. LCM is the method to find the smallest possible multiple of two or more numbers. Teachers recommend students to refer to the article LCM of Two Numbers during exam preparation as it is one of the best guides to clear doubts instantly. Students who want to gain knowledge of the LCM concept must practise the problems using this article on a regular basis. Here, we will learn how to determine the least common multiple of 12 and 19 in a comprehensive manner.
What is LCM of 12 and 19?
The Least Common Multiple of 12 and 19 is 228.
How to Find LCM of 12 and 19?
LCM of 12 and 19 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 12 and 19 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 12 and 19 can be expressed as;
12 = 2 × 2 × 3
19 = 19
LCM (12, 19) = 2 × 2 × 3 × 19 = 228
LCM of 12 and 19 Using Division Method
In the division method, to calculate the least common multiple of 12 and 19, we divide the numbers 12 and 19 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 12 and 19.
| 2 | 12 | 19 |
| 2 | 6 | 19 |
| 3 | 3 | 19 |
| 19 | 1 | 19 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 19) = 2 × 2 × 3 × 19 = 228
LCM of 12 and 19 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 12 and 19 are as follows:
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …….,192, 204, 216, 228,……..
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, ………..
LCM (12, 19) = 228
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 12 and 19?
Solution: 228 is the smallest number that is divisible by both 12 and 19.
2. What is the LCM if the product of two numbers is 228 and their GCD is 1?
Solution: Given
GCD = 1
Product of numbers = 228
We know that
LCM × GCD = Product of numbers
LCM = Product of numbers / GCD
LCM = 228 / 1
LCM = 228
Hence the LCM is 228.
Frequently Asked Questions on LCM of 12 and 19
What is the LCM of 12 and 19?
Is the LCM of 12 and 19 the same as the HCF of 12 and 19?
128 is the LCM of 12 and 19. True or False.
Name the methods used to find the LCM of 12 and 19.
The following methods are used to find the LCM of 12 and 19
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 12 and 19 using prime factorisation.
In this method, we find the prime factors to find the LCM using prime factorisation
12 = 2 × 2 × 3
19 = 19
LCM (12, 19) = 2 × 2 × 3 × 19 = 228
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