Least Common Multiple (LCM) of 59 and 106
The least common multiple (LCM) of 59 and 106 is 6254.
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 106?
First, calculate the GCD of 59 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 106 = 0 remainder 59 |
| 2 | 106 ÷ 59 = 1 remainder 47 |
| 3 | 59 ÷ 47 = 1 remainder 12 |
| 4 | 47 ÷ 12 = 3 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 99 | 3960 |
| 78 and 39 | 78 |
| 86 and 109 | 9374 |
| 160 and 118 | 9440 |
| 122 and 190 | 11590 |