Least Common Multiple (LCM) of 123 and 46
The least common multiple (LCM) of 123 and 46 is 5658.
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 46?
First, calculate the GCD of 123 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 46 = 2 remainder 31 |
| 2 | 46 ÷ 31 = 1 remainder 15 |
| 3 | 31 ÷ 15 = 2 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 192 | 3648 |
| 188 and 92 | 4324 |
| 113 and 77 | 8701 |
| 71 and 192 | 13632 |
| 153 and 196 | 29988 |