Least Common Multiple (LCM) of 102 and 121
The least common multiple (LCM) of 102 and 121 is 12342.
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 121?
First, calculate the GCD of 102 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 121 = 0 remainder 102 |
| 2 | 121 ÷ 102 = 1 remainder 19 |
| 3 | 102 ÷ 19 = 5 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 32 | 800 |
| 18 and 170 | 1530 |
| 29 and 41 | 1189 |
| 142 and 48 | 3408 |
| 162 and 59 | 9558 |