LCM of 9 and 19 is 171. LCM denotes the smallest positive number that is a multiple of two or more numbers. The article Least Common Multiple (LCM) gives a crystal idea of the LCM concept in simple and understandable language for students. If students learn the LCM concept well, performing well in the annual exam will be an easy task. Let us grasp the simple way of denoting the least common multiple of 9 and 19 with solved examples and FAQs here.
What is LCM of 9 and 19?
The Least Common Multiple of 9 and 19 is 171.
How to Find LCM of 9 and 19?
LCM of 9 and 19 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 9 and 19 Using Prime Factorisation Method
In the prime factorisation method, LCM of 9 and 19 can be obtained by multiplying prime factors raised to their respective highest power.
9 = 3 × 3
19 = 19
LCM (9, 19) = 3 × 3 × 19 = 171
LCM of 9 and 19 Using Division Method
In the division method, to find the LCM, we divide the numbers 9 and 19 by their prime factors until we get the result as one in the complete row. The product of these divisors indicates the least common multiple of 9 and 19.
| 3 | 9 | 19 |
| 3 | 3 | 19 |
| 19 | 1 | 19 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 19) = 3 × 3 × 19 = 171
LCM of 9 and 19 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the least common multiple among them. A few multiples of 9 and 19 are shown below.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …………, 153, 162, 171, ……….
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171,……….
LCM (9, 19) = 171
Related Articles
Prime Factorisation 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 9 and 19?
Solution: 171 is the smallest number that is divisible by both 9 and 19.
2. The GCD and LCM of two numbers are 1 and 171 and one number is 9. What is the other number?
Solution: Let the other number be r
We know that
GCD × LCM = 9 × r
r = (GCD × LCM) / 9
r = (1 × 171) / 9
r = 19
Therefore the other number is 19.
Frequently Asked Questions on LCM of 9 and 19
What is the LCM of 9 and 19?
Mention the LCM of 9 and 19 and the HCF of 9 and 19.
Name the methods used to find the least common multiple of 9 and 19.
The following methods are used to find the least common multiple of 9 and 19:
Prime Factorisation
Division method
Listing the Multiples
Determine the LCM of 9 and 19 using prime factorisation.
In prime factorisation, we express the numbers as the product of prime factors to determine the LCM
9 = 3 × 3
19 = 19
LCM (9, 19) = 3 × 3 × 19 = 171
Comments