Least Common Multiple (LCM) of 21 and 186
The least common multiple (LCM) of 21 and 186 is 1302.
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 21 and 186?
First, calculate the GCD of 21 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 186 = 0 remainder 21 |
| 2 | 186 ÷ 21 = 8 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 179 | 18437 |
| 105 and 190 | 3990 |
| 181 and 176 | 31856 |
| 137 and 182 | 24934 |
| 199 and 109 | 21691 |