Least Common Multiple (LCM) of 34 and 123
The least common multiple (LCM) of 34 and 123 is 4182.
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 123?
First, calculate the GCD of 34 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 123 = 0 remainder 34 |
| 2 | 123 ÷ 34 = 3 remainder 21 |
| 3 | 34 ÷ 21 = 1 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 34 | 2414 |
| 136 and 188 | 6392 |
| 84 and 49 | 588 |
| 167 and 39 | 6513 |
| 56 and 84 | 168 |