Least Common Multiple (LCM) of 45 and 122
The least common multiple (LCM) of 45 and 122 is 5490.
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 122?
First, calculate the GCD of 45 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 122 = 0 remainder 45 |
| 2 | 122 ÷ 45 = 2 remainder 32 |
| 3 | 45 ÷ 32 = 1 remainder 13 |
| 4 | 32 ÷ 13 = 2 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 101 | 8585 |
| 102 and 163 | 16626 |
| 189 and 10 | 1890 |
| 51 and 20 | 1020 |
| 113 and 96 | 10848 |