Least Common Multiple (LCM) of 23 and 124
The least common multiple (LCM) of 23 and 124 is 2852.
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 23 and 124?
First, calculate the GCD of 23 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 124 = 0 remainder 23 |
| 2 | 124 ÷ 23 = 5 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 50 | 600 |
| 100 and 174 | 8700 |
| 144 and 101 | 14544 |
| 154 and 67 | 10318 |
| 140 and 140 | 140 |