Least Common Multiple (LCM) of 51 and 122
The least common multiple (LCM) of 51 and 122 is 6222.
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 51 and 122?
First, calculate the GCD of 51 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 122 = 0 remainder 51 |
| 2 | 122 ÷ 51 = 2 remainder 20 |
| 3 | 51 ÷ 20 = 2 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 110 | 330 |
| 41 and 34 | 1394 |
| 25 and 64 | 1600 |
| 138 and 82 | 5658 |
| 134 and 55 | 7370 |