Least Common Multiple (LCM) of 59 and 45
The least common multiple (LCM) of 59 and 45 is 2655.
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 45?
First, calculate the GCD of 59 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 45 = 1 remainder 14 |
| 2 | 45 ÷ 14 = 3 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 26 | 2626 |
| 99 and 141 | 4653 |
| 110 and 40 | 440 |
| 107 and 151 | 16157 |
| 57 and 98 | 5586 |