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 |
|---|---|
| 89 and 155 | 13795 |
| 115 and 144 | 16560 |
| 164 and 122 | 10004 |
| 119 and 71 | 8449 |
| 135 and 141 | 6345 |