Least Common Multiple (LCM) of 63 and 123
The least common multiple (LCM) of 63 and 123 is 2583.
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 123?
First, calculate the GCD of 63 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 123 = 0 remainder 63 |
| 2 | 123 ÷ 63 = 1 remainder 60 |
| 3 | 63 ÷ 60 = 1 remainder 3 |
| 4 | 60 ÷ 3 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 157 | 28103 |
| 160 and 129 | 20640 |
| 38 and 135 | 5130 |
| 100 and 183 | 18300 |
| 50 and 66 | 1650 |