Least Common Multiple (LCM) of 34 and 124
The least common multiple (LCM) of 34 and 124 is 2108.
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 34 and 124?
First, calculate the GCD of 34 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 124 = 0 remainder 34 |
| 2 | 124 ÷ 34 = 3 remainder 22 |
| 3 | 34 ÷ 22 = 1 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 117 | 5031 |
| 91 and 48 | 4368 |
| 100 and 70 | 700 |
| 40 and 17 | 680 |
| 177 and 27 | 1593 |