Least Common Multiple (LCM) of 123 and 105
The least common multiple (LCM) of 123 and 105 is 4305.
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 105?
First, calculate the GCD of 123 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 105 = 1 remainder 18 |
| 2 | 105 ÷ 18 = 5 remainder 15 |
| 3 | 18 ÷ 15 = 1 remainder 3 |
| 4 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 111 | 14097 |
| 104 and 106 | 5512 |
| 188 and 147 | 27636 |
| 72 and 195 | 4680 |
| 67 and 137 | 9179 |