Least Common Multiple (LCM) of 100 and 186
The least common multiple (LCM) of 100 and 186 is 9300.
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 186?
First, calculate the GCD of 100 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 186 = 0 remainder 100 |
| 2 | 186 ÷ 100 = 1 remainder 86 |
| 3 | 100 ÷ 86 = 1 remainder 14 |
| 4 | 86 ÷ 14 = 6 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 137 | 9316 |
| 29 and 112 | 3248 |
| 175 and 86 | 15050 |
| 191 and 25 | 4775 |
| 78 and 180 | 2340 |