LCM of 13 and 19 is 247. The lowest common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. The detailed explanation provided in the article Least Common Multiple (LCM) improves students’ analytical and logical thinking abilities. Learning the LCM concept thoroughly helps students to solve problems of higher difficulty levels with ease. Let us glance at the simple steps to calculate the least common multiple of 13 and 19 here.
What is LCM of 13 and 19?
The Least Common Multiple of 13 and 19 is 247.
How to Find LCM of 13 and 19?
The LCM of 13 and 19 can be determined by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 13 and 19 Using Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Hence the numbers 13 and 19 can be expressed as;
13 = 13
19 = 19
LCM (13, 19) = 13 × 19 = 247
LCM of 13 and 19 Using Division Method
In the division method, to find the LCM, we divide the numbers 13 and 19 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 13 and 19.
| 13 | 13 | 19 |
| 19 | 1 | 19 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (13, 19) = 13 × 19 = 247
LCM of 13 and 19 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the least common multiple among them. Let us glance at the multiples of 13 and 19 given below.
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, …….,221, 234, 247, ………
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, …………
LCM (13, 19) = 247
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 13 and 19?
Solution: 247 is the smallest number that is divisible by both 13 and 19.
2. The GCD and LCM of the two numbers are 1 and 247. If one number is 13, what is the other number?
Solution: Let the other number be p
We know that,
GCD × LCM = 13 × p
p = (GCD × LCM) / 13
p = (1 × 247) / 13
p = 19
Hence, the other number is 19.
Frequently Asked Questions on LCM of 13 and 19
What is the LCM of 13 and 19?
Is the LCM of 13 and 19 the same as the HCF of 13 and 19?
267 is the LCM of 13 and 19. True or False.
What are the methods used to find the LCM of 13 and 19?
The methods used to find the LCM of 13 and 19 are
Prime Factorisation
Division Method
Listing the Multiples
Mention the relation between the GCF and LCM of 13 and 19.
The below equation can be used to represent the relation between GCF and LCM of 13 and 19 is
GCF × LCM = 13 × 19
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