Least Common Multiple (LCM) of 21 and 122
The least common multiple (LCM) of 21 and 122 is 2562.
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 122?
First, calculate the GCD of 21 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 122 = 0 remainder 21 |
| 2 | 122 ÷ 21 = 5 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 |
|---|---|
| 128 and 178 | 11392 |
| 126 and 140 | 1260 |
| 176 and 199 | 35024 |
| 179 and 134 | 23986 |
| 135 and 19 | 2565 |