Least Common Multiple (LCM) of 105 and 124
The least common multiple (LCM) of 105 and 124 is 13020.
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 105 and 124?
First, calculate the GCD of 105 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 124 = 0 remainder 105 |
| 2 | 124 ÷ 105 = 1 remainder 19 |
| 3 | 105 ÷ 19 = 5 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 173 | 6747 |
| 75 and 173 | 12975 |
| 132 and 24 | 264 |
| 173 and 100 | 17300 |
| 91 and 14 | 182 |