Least Common Multiple (LCM) of 97 and 123
The least common multiple (LCM) of 97 and 123 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 97 and 123?
First, calculate the GCD of 97 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 123 = 0 remainder 97 |
| 2 | 123 ÷ 97 = 1 remainder 26 |
| 3 | 97 ÷ 26 = 3 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 137 | 15344 |
| 161 and 153 | 24633 |
| 148 and 60 | 2220 |
| 15 and 123 | 615 |
| 66 and 157 | 10362 |