Least Common Multiple (LCM) of 122 and 76
The least common multiple (LCM) of 122 and 76 is 4636.
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 122 and 76?
First, calculate the GCD of 122 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 76 = 1 remainder 46 |
| 2 | 76 ÷ 46 = 1 remainder 30 |
| 3 | 46 ÷ 30 = 1 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 136 | 14280 |
| 78 and 195 | 390 |
| 137 and 179 | 24523 |
| 33 and 178 | 5874 |
| 51 and 171 | 2907 |