Least Common Multiple (LCM) of 34 and 126
The least common multiple (LCM) of 34 and 126 is 2142.
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 126?
First, calculate the GCD of 34 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 126 = 0 remainder 34 |
| 2 | 126 ÷ 34 = 3 remainder 24 |
| 3 | 34 ÷ 24 = 1 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 52 | 1456 |
| 175 and 54 | 9450 |
| 51 and 200 | 10200 |
| 138 and 113 | 15594 |
| 38 and 121 | 4598 |