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 |
|---|---|
| 107 and 194 | 20758 |
| 149 and 140 | 20860 |
| 186 and 194 | 18042 |
| 59 and 73 | 4307 |
| 174 and 26 | 2262 |