Least Common Multiple (LCM) of 45 and 121
The least common multiple (LCM) of 45 and 121 is 5445.
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 45 and 121?
First, calculate the GCD of 45 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 121 = 0 remainder 45 |
| 2 | 121 ÷ 45 = 2 remainder 31 |
| 3 | 45 ÷ 31 = 1 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 117 | 936 |
| 51 and 38 | 1938 |
| 159 and 99 | 5247 |
| 62 and 60 | 1860 |
| 54 and 135 | 270 |