Least Common Multiple (LCM) of 123 and 63
The least common multiple (LCM) of 123 and 63 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 123 and 63?
First, calculate the GCD of 123 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 63 = 1 remainder 60 |
| 2 | 63 ÷ 60 = 1 remainder 3 |
| 3 | 60 ÷ 3 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 160 | 2400 |
| 35 and 196 | 980 |
| 125 and 42 | 5250 |
| 101 and 113 | 11413 |
| 142 and 155 | 22010 |