Least Common Multiple (LCM) of 157 and 65
The least common multiple (LCM) of 157 and 65 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 157 and 65?
First, calculate the GCD of 157 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 65 = 2 remainder 27 |
| 2 | 65 ÷ 27 = 2 remainder 11 |
| 3 | 27 ÷ 11 = 2 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 89 | 11570 |
| 200 and 168 | 4200 |
| 155 and 102 | 15810 |
| 16 and 14 | 112 |
| 17 and 76 | 1292 |