Least Common Multiple (LCM) of 120 and 97
The least common multiple (LCM) of 120 and 97 is 11640.
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 120 and 97?
First, calculate the GCD of 120 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 97 = 1 remainder 23 |
| 2 | 97 ÷ 23 = 4 remainder 5 |
| 3 | 23 ÷ 5 = 4 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 146 | 15622 |
| 54 and 61 | 3294 |
| 18 and 195 | 1170 |
| 107 and 75 | 8025 |
| 143 and 163 | 23309 |