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 |
|---|---|
| 80 and 187 | 14960 |
| 126 and 174 | 3654 |
| 101 and 165 | 16665 |
| 107 and 84 | 8988 |
| 32 and 138 | 2208 |