Least Common Multiple (LCM) of 102 and 122
The least common multiple (LCM) of 102 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 102 and 122?
First, calculate the GCD of 102 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 122 = 0 remainder 102 |
| 2 | 122 ÷ 102 = 1 remainder 20 |
| 3 | 102 ÷ 20 = 5 remainder 2 |
| 4 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 30 | 30 |
| 12 and 13 | 156 |
| 93 and 138 | 4278 |
| 150 and 87 | 4350 |
| 57 and 185 | 10545 |