Least Common Multiple (LCM) of 59 and 117
The least common multiple (LCM) of 59 and 117 is 6903.
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 117?
First, calculate the GCD of 59 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 117 = 0 remainder 59 |
| 2 | 117 ÷ 59 = 1 remainder 58 |
| 3 | 59 ÷ 58 = 1 remainder 1 |
| 4 | 58 ÷ 1 = 58 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 171 | 28044 |
| 30 and 133 | 3990 |
| 84 and 166 | 6972 |
| 124 and 67 | 8308 |
| 186 and 47 | 8742 |