Least Common Multiple (LCM) of 123 and 73
The least common multiple (LCM) of 123 and 73 is 8979.
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 73?
First, calculate the GCD of 123 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 73 = 1 remainder 50 |
| 2 | 73 ÷ 50 = 1 remainder 23 |
| 3 | 50 ÷ 23 = 2 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 36 | 1116 |
| 184 and 95 | 17480 |
| 96 and 49 | 4704 |
| 67 and 86 | 5762 |
| 160 and 197 | 31520 |