Least Common Multiple (LCM) of 102 and 123
The least common multiple (LCM) of 102 and 123 is 4182.
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 123?
First, calculate the GCD of 102 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 123 = 0 remainder 102 |
| 2 | 123 ÷ 102 = 1 remainder 21 |
| 3 | 102 ÷ 21 = 4 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 98 | 7938 |
| 36 and 118 | 2124 |
| 36 and 80 | 720 |
| 153 and 89 | 13617 |
| 185 and 105 | 3885 |