Least Common Multiple (LCM) of 63 and 122
The least common multiple (LCM) of 63 and 122 is 7686.
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 63 and 122?
First, calculate the GCD of 63 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 122 = 0 remainder 63 |
| 2 | 122 ÷ 63 = 1 remainder 59 |
| 3 | 63 ÷ 59 = 1 remainder 4 |
| 4 | 59 ÷ 4 = 14 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 25 | 450 |
| 142 and 183 | 25986 |
| 52 and 160 | 2080 |
| 127 and 36 | 4572 |
| 64 and 135 | 8640 |