Least Common Multiple (LCM) of 124 and 189
The least common multiple (LCM) of 124 and 189 is 23436.
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 124 and 189?
First, calculate the GCD of 124 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 124 ÷ 189 = 0 remainder 124 |
| 2 | 189 ÷ 124 = 1 remainder 65 |
| 3 | 124 ÷ 65 = 1 remainder 59 |
| 4 | 65 ÷ 59 = 1 remainder 6 |
| 5 | 59 ÷ 6 = 9 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 75 | 11400 |
| 24 and 89 | 2136 |
| 96 and 29 | 2784 |
| 180 and 123 | 7380 |
| 104 and 69 | 7176 |