Least Common Multiple (LCM) of 122 and 78
The least common multiple (LCM) of 122 and 78 is 4758.
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 78?
First, calculate the GCD of 122 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 78 = 1 remainder 44 |
| 2 | 78 ÷ 44 = 1 remainder 34 |
| 3 | 44 ÷ 34 = 1 remainder 10 |
| 4 | 34 ÷ 10 = 3 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 75 | 9150 |
| 114 and 125 | 14250 |
| 130 and 131 | 17030 |
| 183 and 115 | 21045 |
| 80 and 170 | 1360 |