Least Common Multiple (LCM) of 59 and 97
The least common multiple (LCM) of 59 and 97 is 5723.
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 59 and 97?
First, calculate the GCD of 59 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 97 = 0 remainder 59 |
| 2 | 97 ÷ 59 = 1 remainder 38 |
| 3 | 59 ÷ 38 = 1 remainder 21 |
| 4 | 38 ÷ 21 = 1 remainder 17 |
| 5 | 21 ÷ 17 = 1 remainder 4 |
| 6 | 17 ÷ 4 = 4 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 132 | 2244 |
| 189 and 37 | 6993 |
| 74 and 18 | 666 |
| 75 and 77 | 5775 |
| 10 and 112 | 560 |