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 |
|---|---|
| 10 and 110 | 110 |
| 131 and 199 | 26069 |
| 50 and 27 | 1350 |
| 10 and 38 | 190 |
| 161 and 28 | 644 |