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 |
|---|---|
| 141 and 129 | 6063 |
| 124 and 111 | 13764 |
| 126 and 85 | 10710 |
| 92 and 90 | 4140 |
| 180 and 142 | 12780 |