Least Common Multiple (LCM) of 125 and 77
The least common multiple (LCM) of 125 and 77 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 125 and 77?
First, calculate the GCD of 125 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 77 = 1 remainder 48 |
| 2 | 77 ÷ 48 = 1 remainder 29 |
| 3 | 48 ÷ 29 = 1 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 135 | 7020 |
| 82 and 57 | 4674 |
| 10 and 157 | 1570 |
| 159 and 144 | 7632 |
| 80 and 48 | 240 |