Least Common Multiple (LCM) of 77 and 171
The least common multiple (LCM) of 77 and 171 is 13167.
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 171?
First, calculate the GCD of 77 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 171 = 0 remainder 77 |
| 2 | 171 ÷ 77 = 2 remainder 17 |
| 3 | 77 ÷ 17 = 4 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 16 | 1776 |
| 135 and 73 | 9855 |
| 137 and 57 | 7809 |
| 142 and 78 | 5538 |
| 192 and 143 | 27456 |