Least Common Multiple (LCM) of 100 and 185
The least common multiple (LCM) of 100 and 185 is 3700.
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 185?
First, calculate the GCD of 100 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 185 = 0 remainder 100 |
| 2 | 185 ÷ 100 = 1 remainder 85 |
| 3 | 100 ÷ 85 = 1 remainder 15 |
| 4 | 85 ÷ 15 = 5 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 77 | 231 |
| 67 and 141 | 9447 |
| 37 and 100 | 3700 |
| 131 and 77 | 10087 |
| 182 and 197 | 35854 |