Least Common Multiple (LCM) of 97 and 120
The least common multiple (LCM) of 97 and 120 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 97 and 120?
First, calculate the GCD of 97 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 120 = 0 remainder 97 |
| 2 | 120 ÷ 97 = 1 remainder 23 |
| 3 | 97 ÷ 23 = 4 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 11 | 1309 |
| 144 and 106 | 7632 |
| 103 and 157 | 16171 |
| 53 and 49 | 2597 |
| 99 and 182 | 18018 |