Least Common Multiple (LCM) of 15 and 122
The least common multiple (LCM) of 15 and 122 is 1830.
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 15 and 122?
First, calculate the GCD of 15 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 122 = 0 remainder 15 |
| 2 | 122 ÷ 15 = 8 remainder 2 |
| 3 | 15 ÷ 2 = 7 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 189 | 945 |
| 36 and 35 | 1260 |
| 114 and 112 | 6384 |
| 72 and 176 | 1584 |
| 122 and 65 | 7930 |