Least Common Multiple (LCM) of 77 and 141
The least common multiple (LCM) of 77 and 141 is 10857.
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 141?
First, calculate the GCD of 77 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 141 = 0 remainder 77 |
| 2 | 141 ÷ 77 = 1 remainder 64 |
| 3 | 77 ÷ 64 = 1 remainder 13 |
| 4 | 64 ÷ 13 = 4 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 192 | 960 |
| 109 and 131 | 14279 |
| 31 and 193 | 5983 |
| 164 and 11 | 1804 |
| 24 and 69 | 552 |