Least Common Multiple (LCM) of 59 and 132
The least common multiple (LCM) of 59 and 132 is 7788.
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 132?
First, calculate the GCD of 59 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 132 = 0 remainder 59 |
| 2 | 132 ÷ 59 = 2 remainder 14 |
| 3 | 59 ÷ 14 = 4 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 29 | 3161 |
| 23 and 55 | 1265 |
| 10 and 132 | 660 |
| 19 and 80 | 1520 |
| 117 and 71 | 8307 |