LCM of 100 and 190 is 1900. The LCM is the method to find the least common multiple between any two or more numbers. Prime Factorisation and Division Method for LCM and HCF is a vital study material for the students which helps them to grasp the concept thoroughly. Time management skills can be improved among the students by practising the problems using this article prepared by experts. Let us learn the method of finding the least common multiple of 100 and 190 using suitable examples and FAQs here.
What is LCM of 100 and 190?
The Least Common Multiple of 100 and 190 is 1900.
How to Find LCM of 100 and 190?
LCM of 100 and 190 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 100 and 190 Using Prime Factorisation Method
In the prime factorisation method, LCM of 100 and 190 can be obtained by multiplying prime factors raised to their respective highest power.
100 = 2 × 2 × 5 × 5
190 = 2 × 5 × 19
LCM (100, 190) = 2 × 2 × 5 × 5 × 19 = 1900
LCM of 100 and 190 Using Division Method
In the division method, to calculate the least common multiple of 100 and 190, we divide the numbers 100 and 190 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 100 and 190.
| 2 | 100 | 190 |
| 2 | 50 | 95 |
| 5 | 25 | 95 |
| 5 | 5 | 19 |
| 19 | 1 | 19 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (100, 190) = 2 × 2 × 5 × 5 × 19 = 1900
LCM of 100 and 190 Using Listing the Multiples
In this method, we list down the multiples of 100 and 190 to find the least common multiple among them. The following list shows the multiples of 100 and 190.
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, ……, 1700, 1800, 1900,….
Multiples of 190: 190, 380, 570, 760, 950, 1140, 1330, 1520, 1710, 1900, ………
LCM (100, 190) = 1900
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Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 100 and 190?
Solution: 1900 is the smallest number that is divisible by both 100 and 190.
2. The GCD and LCM of the two numbers are 10 and 1900. If one number is 100, what is the other number?
Solution: Let the other number be k
We know that,
GCD × LCM = 100 × k
k = (GCD × LCM) / 100
k = (10 × 1900) / 100
k = 190
Hence the other number is 190.
Frequently Asked Questions on LCM of 100 and 190
What is the LCM of 100 and 190?
Is the LCM of 100 and 190 the same as the HCF of 100 and 190?
Name the methods used to find the LCM of 100 and 190.
The methods used to find the LCM of 100 and 190 are as follows:
Prime Factorisation
Division method
Listing the Multiples
Mention the relation between the GCF and LCM of 100 and 190.
The relation between the GCF and the LCM of 100 and 190 is
GCF × LCM = 100 × 190
GCF × LCM = 19000
Determine the GCF if the LCM of 100 and 190 is 1900.
GCF × LCM = 100 × 190
Given
LCM = 1900
GCF × 1900 = 100 x 190
GCF = 10
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