Least Common Multiple (LCM) of 142 and 77
The least common multiple (LCM) of 142 and 77 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 142 and 77?
First, calculate the GCD of 142 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 77 = 1 remainder 65 |
| 2 | 77 ÷ 65 = 1 remainder 12 |
| 3 | 65 ÷ 12 = 5 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 14 | 1638 |
| 40 and 52 | 520 |
| 148 and 121 | 17908 |
| 57 and 187 | 10659 |
| 117 and 123 | 4797 |