Least Common Multiple (LCM) of 21 and 185
The least common multiple (LCM) of 21 and 185 is 3885.
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 185?
First, calculate the GCD of 21 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 185 = 0 remainder 21 |
| 2 | 185 ÷ 21 = 8 remainder 17 |
| 3 | 21 ÷ 17 = 1 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 88 | 2552 |
| 196 and 139 | 27244 |
| 141 and 82 | 11562 |
| 13 and 183 | 2379 |
| 133 and 17 | 2261 |