Least Common Multiple (LCM) of 29 and 142
The least common multiple (LCM) of 29 and 142 is 4118.
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 29 and 142?
First, calculate the GCD of 29 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 142 = 0 remainder 29 |
| 2 | 142 ÷ 29 = 4 remainder 26 |
| 3 | 29 ÷ 26 = 1 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 73 | 5110 |
| 177 and 53 | 9381 |
| 97 and 64 | 6208 |
| 159 and 174 | 9222 |
| 110 and 135 | 2970 |