Least Common Multiple (LCM) of 135 and 154
The least common multiple (LCM) of 135 and 154 is 20790.
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 154?
First, calculate the GCD of 135 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 154 = 0 remainder 135 |
| 2 | 154 ÷ 135 = 1 remainder 19 |
| 3 | 135 ÷ 19 = 7 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 90 | 990 |
| 188 and 123 | 23124 |
| 73 and 109 | 7957 |
| 136 and 35 | 4760 |
| 52 and 182 | 364 |