Least Common Multiple (LCM) of 121 and 135
The least common multiple (LCM) of 121 and 135 is 16335.
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 121 and 135?
First, calculate the GCD of 121 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 135 = 0 remainder 121 |
| 2 | 135 ÷ 121 = 1 remainder 14 |
| 3 | 121 ÷ 14 = 8 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 162 | 5670 |
| 180 and 189 | 3780 |
| 109 and 181 | 19729 |
| 146 and 36 | 2628 |
| 75 and 26 | 1950 |