Least Common Multiple (LCM) of 169 and 123
The least common multiple (LCM) of 169 and 123 is 20787.
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 169 and 123?
First, calculate the GCD of 169 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 123 = 1 remainder 46 |
| 2 | 123 ÷ 46 = 2 remainder 31 |
| 3 | 46 ÷ 31 = 1 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 161 | 322 |
| 46 and 75 | 3450 |
| 131 and 33 | 4323 |
| 104 and 36 | 936 |
| 102 and 90 | 1530 |