Least Common Multiple (LCM) of 59 and 141
The least common multiple (LCM) of 59 and 141 is 8319.
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 141?
First, calculate the GCD of 59 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 141 = 0 remainder 59 |
| 2 | 141 ÷ 59 = 2 remainder 23 |
| 3 | 59 ÷ 23 = 2 remainder 13 |
| 4 | 23 ÷ 13 = 1 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 110 | 660 |
| 56 and 143 | 8008 |
| 75 and 43 | 3225 |
| 54 and 37 | 1998 |
| 16 and 180 | 720 |