Least Common Multiple (LCM) of 123 and 140
The least common multiple (LCM) of 123 and 140 is 17220.
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 140?
First, calculate the GCD of 123 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 140 = 0 remainder 123 |
| 2 | 140 ÷ 123 = 1 remainder 17 |
| 3 | 123 ÷ 17 = 7 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 142 | 4260 |
| 100 and 108 | 2700 |
| 109 and 146 | 15914 |
| 125 and 32 | 4000 |
| 158 and 162 | 12798 |