Least Common Multiple (LCM) of 123 and 84
The least common multiple (LCM) of 123 and 84 is 3444.
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 84?
First, calculate the GCD of 123 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 84 = 1 remainder 39 |
| 2 | 84 ÷ 39 = 2 remainder 6 |
| 3 | 39 ÷ 6 = 6 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 14 | 1806 |
| 30 and 101 | 3030 |
| 147 and 183 | 8967 |
| 108 and 24 | 216 |
| 193 and 108 | 20844 |