Least Common Multiple (LCM) of 123 and 97
The least common multiple (LCM) of 123 and 97 is 11931.
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 97?
First, calculate the GCD of 123 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 97 = 1 remainder 26 |
| 2 | 97 ÷ 26 = 3 remainder 19 |
| 3 | 26 ÷ 19 = 1 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 127 | 5969 |
| 164 and 91 | 14924 |
| 172 and 143 | 24596 |
| 75 and 192 | 4800 |
| 198 and 69 | 4554 |