Least Common Multiple (LCM) of 21 and 124
The least common multiple (LCM) of 21 and 124 is 2604.
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 124?
First, calculate the GCD of 21 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 124 = 0 remainder 21 |
| 2 | 124 ÷ 21 = 5 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 179 | 35263 |
| 47 and 34 | 1598 |
| 22 and 113 | 2486 |
| 14 and 71 | 994 |
| 172 and 178 | 15308 |