Least Common Multiple (LCM) of 77 and 143
The least common multiple (LCM) of 77 and 143 is 1001.
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 143?
First, calculate the GCD of 77 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 143 = 0 remainder 77 |
| 2 | 143 ÷ 77 = 1 remainder 66 |
| 3 | 77 ÷ 66 = 1 remainder 11 |
| 4 | 66 ÷ 11 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 20 | 340 |
| 190 and 61 | 11590 |
| 49 and 89 | 4361 |
| 188 and 63 | 11844 |
| 115 and 54 | 6210 |