Least Common Multiple (LCM) of 123 and 142
The least common multiple (LCM) of 123 and 142 is 17466.
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 142?
First, calculate the GCD of 123 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 142 = 0 remainder 123 |
| 2 | 142 ÷ 123 = 1 remainder 19 |
| 3 | 123 ÷ 19 = 6 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 20 | 1220 |
| 74 and 130 | 4810 |
| 40 and 41 | 1640 |
| 75 and 167 | 12525 |
| 51 and 54 | 918 |