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 |
|---|---|
| 172 and 191 | 32852 |
| 35 and 49 | 245 |
| 182 and 40 | 3640 |
| 101 and 68 | 6868 |
| 133 and 114 | 798 |