Least Common Multiple (LCM) of 135 and 157
The least common multiple (LCM) of 135 and 157 is 21195.
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 135 and 157?
First, calculate the GCD of 135 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 157 = 0 remainder 135 |
| 2 | 157 ÷ 135 = 1 remainder 22 |
| 3 | 135 ÷ 22 = 6 remainder 3 |
| 4 | 22 ÷ 3 = 7 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 164 | 3444 |
| 64 and 142 | 4544 |
| 63 and 162 | 1134 |
| 14 and 171 | 2394 |
| 128 and 15 | 1920 |