Least Common Multiple (LCM) of 99 and 59
The least common multiple (LCM) of 99 and 59 is 5841.
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 99 and 59?
First, calculate the GCD of 99 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 59 = 1 remainder 40 |
| 2 | 59 ÷ 40 = 1 remainder 19 |
| 3 | 40 ÷ 19 = 2 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 20 | 1660 |
| 78 and 157 | 12246 |
| 128 and 199 | 25472 |
| 105 and 144 | 5040 |
| 140 and 39 | 5460 |