Least Common Multiple (LCM) of 77 and 157
The least common multiple (LCM) of 77 and 157 is 12089.
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 157?
First, calculate the GCD of 77 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 157 = 0 remainder 77 |
| 2 | 157 ÷ 77 = 2 remainder 3 |
| 3 | 77 ÷ 3 = 25 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 63 | 8064 |
| 170 and 77 | 13090 |
| 62 and 172 | 5332 |
| 177 and 99 | 5841 |
| 106 and 134 | 7102 |