Least Common Multiple (LCM) of 59 and 188
The least common multiple (LCM) of 59 and 188 is 11092.
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 188?
First, calculate the GCD of 59 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 188 = 0 remainder 59 |
| 2 | 188 ÷ 59 = 3 remainder 11 |
| 3 | 59 ÷ 11 = 5 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 160 | 7840 |
| 15 and 142 | 2130 |
| 120 and 56 | 840 |
| 21 and 137 | 2877 |
| 85 and 104 | 8840 |