Least Common Multiple (LCM) of 123 and 169
The least common multiple (LCM) of 123 and 169 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 123 and 169?
First, calculate the GCD of 123 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 169 = 0 remainder 123 |
| 2 | 169 ÷ 123 = 1 remainder 46 |
| 3 | 123 ÷ 46 = 2 remainder 31 |
| 4 | 46 ÷ 31 = 1 remainder 15 |
| 5 | 31 ÷ 15 = 2 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 47 | 3807 |
| 162 and 57 | 3078 |
| 30 and 155 | 930 |
| 54 and 33 | 594 |
| 175 and 109 | 19075 |