Least Common Multiple (LCM) of 77 and 131
The least common multiple (LCM) of 77 and 131 is 10087.
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 131?
First, calculate the GCD of 77 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 131 = 0 remainder 77 |
| 2 | 131 ÷ 77 = 1 remainder 54 |
| 3 | 77 ÷ 54 = 1 remainder 23 |
| 4 | 54 ÷ 23 = 2 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 117 | 1170 |
| 160 and 171 | 27360 |
| 155 and 113 | 17515 |
| 45 and 106 | 4770 |
| 174 and 192 | 5568 |