Least Common Multiple (LCM) of 77 and 125
The least common multiple (LCM) of 77 and 125 is 9625.
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 125?
First, calculate the GCD of 77 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 125 = 0 remainder 77 |
| 2 | 125 ÷ 77 = 1 remainder 48 |
| 3 | 77 ÷ 48 = 1 remainder 29 |
| 4 | 48 ÷ 29 = 1 remainder 19 |
| 5 | 29 ÷ 19 = 1 remainder 10 |
| 6 | 19 ÷ 10 = 1 remainder 9 |
| 7 | 10 ÷ 9 = 1 remainder 1 |
| 8 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 20 | 540 |
| 84 and 128 | 2688 |
| 119 and 72 | 8568 |
| 120 and 113 | 13560 |
| 132 and 93 | 4092 |