Least Common Multiple (LCM) of 34 and 142
The least common multiple (LCM) of 34 and 142 is 2414.
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 142?
First, calculate the GCD of 34 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 142 = 0 remainder 34 |
| 2 | 142 ÷ 34 = 4 remainder 6 |
| 3 | 34 ÷ 6 = 5 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 120 | 840 |
| 95 and 137 | 13015 |
| 101 and 108 | 10908 |
| 54 and 85 | 4590 |
| 53 and 168 | 8904 |