Least Common Multiple (LCM) of 117 and 59
The least common multiple (LCM) of 117 and 59 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 117 and 59?
First, calculate the GCD of 117 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 59 = 1 remainder 58 |
| 2 | 59 ÷ 58 = 1 remainder 1 |
| 3 | 58 ÷ 1 = 58 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 52 | 5876 |
| 79 and 142 | 11218 |
| 145 and 147 | 21315 |
| 108 and 160 | 4320 |
| 16 and 162 | 1296 |