Least Common Multiple (LCM) of 59 and 145
The least common multiple (LCM) of 59 and 145 is 8555.
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 145?
First, calculate the GCD of 59 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 145 = 0 remainder 59 |
| 2 | 145 ÷ 59 = 2 remainder 27 |
| 3 | 59 ÷ 27 = 2 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 187 | 5610 |
| 136 and 79 | 10744 |
| 96 and 17 | 1632 |
| 115 and 16 | 1840 |
| 147 and 80 | 11760 |