Least Common Multiple (LCM) of 100 and 191
The least common multiple (LCM) of 100 and 191 is 19100.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 100 and 191?
First, calculate the GCD of 100 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 191 = 0 remainder 100 |
| 2 | 191 ÷ 100 = 1 remainder 91 |
| 3 | 100 ÷ 91 = 1 remainder 9 |
| 4 | 91 ÷ 9 = 10 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 70 | 5810 |
| 65 and 12 | 780 |
| 36 and 169 | 6084 |
| 142 and 200 | 14200 |
| 75 and 61 | 4575 |