Least Common Multiple (LCM) of 21 and 57
The least common multiple (LCM) of 21 and 57 is 399.
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 57?
First, calculate the GCD of 21 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 57 = 0 remainder 21 |
| 2 | 57 ÷ 21 = 2 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 157 | 12089 |
| 136 and 61 | 8296 |
| 171 and 131 | 22401 |
| 191 and 133 | 25403 |
| 84 and 42 | 84 |