Least Common Multiple (LCM) of 77 and 142
The least common multiple (LCM) of 77 and 142 is 10934.
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 77 and 142?
First, calculate the GCD of 77 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 142 = 0 remainder 77 |
| 2 | 142 ÷ 77 = 1 remainder 65 |
| 3 | 77 ÷ 65 = 1 remainder 12 |
| 4 | 65 ÷ 12 = 5 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 142 | 13774 |
| 21 and 27 | 189 |
| 17 and 197 | 3349 |
| 123 and 135 | 5535 |
| 108 and 156 | 1404 |