Least Common Multiple (LCM) of 123 and 74
The least common multiple (LCM) of 123 and 74 is 9102.
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 74?
First, calculate the GCD of 123 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 74 = 1 remainder 49 |
| 2 | 74 ÷ 49 = 1 remainder 25 |
| 3 | 49 ÷ 25 = 1 remainder 24 |
| 4 | 25 ÷ 24 = 1 remainder 1 |
| 5 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 24 | 792 |
| 59 and 94 | 5546 |
| 78 and 123 | 3198 |
| 75 and 88 | 6600 |
| 171 and 55 | 9405 |