Least Common Multiple (LCM) of 123 and 145
The least common multiple (LCM) of 123 and 145 is 17835.
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 145?
First, calculate the GCD of 123 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 145 = 0 remainder 123 |
| 2 | 145 ÷ 123 = 1 remainder 22 |
| 3 | 123 ÷ 22 = 5 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 64 | 4032 |
| 76 and 21 | 1596 |
| 12 and 115 | 1380 |
| 100 and 59 | 5900 |
| 16 and 172 | 688 |