Least Common Multiple (LCM) of 47 and 117
The least common multiple (LCM) of 47 and 117 is 5499.
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 47 and 117?
First, calculate the GCD of 47 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 117 = 0 remainder 47 |
| 2 | 117 ÷ 47 = 2 remainder 23 |
| 3 | 47 ÷ 23 = 2 remainder 1 |
| 4 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 140 | 21140 |
| 163 and 107 | 17441 |
| 100 and 89 | 8900 |
| 154 and 108 | 8316 |
| 65 and 125 | 1625 |