Least Common Multiple (LCM) of 65 and 157
The least common multiple (LCM) of 65 and 157 is 10205.
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 65 and 157?
First, calculate the GCD of 65 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 157 = 0 remainder 65 |
| 2 | 157 ÷ 65 = 2 remainder 27 |
| 3 | 65 ÷ 27 = 2 remainder 11 |
| 4 | 27 ÷ 11 = 2 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 34 | 374 |
| 53 and 41 | 2173 |
| 106 and 42 | 2226 |
| 114 and 191 | 21774 |
| 71 and 106 | 7526 |