Least Common Multiple (LCM) of 123 and 76
The least common multiple (LCM) of 123 and 76 is 9348.
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 76?
First, calculate the GCD of 123 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 76 = 1 remainder 47 |
| 2 | 76 ÷ 47 = 1 remainder 29 |
| 3 | 47 ÷ 29 = 1 remainder 18 |
| 4 | 29 ÷ 18 = 1 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 34 | 374 |
| 50 and 10 | 50 |
| 191 and 123 | 23493 |
| 187 and 29 | 5423 |
| 114 and 176 | 10032 |